Answer:
a) IQ scores of 94.2 and below represent the bottom 35%.
b) An IQ score of 110.1 represents the 3rd quartile.
c) IQ scores of 124.7 and higher are in the top 5%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
(a) Find the IQ scores that represent the bottom 35%.
The 35th percentile and below, in which the 35th percentile is X when Z has a p-value of 0.35, so X when Z = -0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.385 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = -0.385*15[/tex]
[tex]X = 94.2[/tex]
IQ scores of 94.2 and below represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
This is the 100*3/4 = 75th percentile, which is X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 0.675*15[/tex]
[tex]X = 110.1[/tex]
An IQ score of 110.1 represents the 3rd quartile.
(c) Find the IQ score for the top 5%.
IQ scores of at least the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 1.645*15[/tex]
[tex]X = 124.7[/tex]
IQ scores of 124.7 and higher are in the top 5%.
Charles spent 1/4 of his allowance on a shirt, and 2/5 of the remainder on a book. A.What fraction of his allowance did he have left? B.If he spent $18 on the book, how much did he have at first?
Answer:
18.65
Step-by-step explanation:
1/4+2/5+18=18.65
18.65
hope it helps you good luck
If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4
PLEASE HELP NEED ASAPPPPPPP
Answer:
a and b are positive
Step-by-step explanation:
We are given that
[tex]a-3>b-3[/tex]
[tex]b>4[/tex]
We have to find that a and b are positive or negative.
We have
[tex]b>4[/tex]
It means b is positive and greater than 4.
[tex]a-3>b-3[/tex]
Adding 3 on both sides
[tex]a-3+3>b-3+3[/tex]
[tex]a>b>4[/tex]
[tex]\implies a>4[/tex]
Hence, a is positive and greater than 4.
Therefore, a and b are positive
1/2-5(2/3x + 6)+4/5x?
Answer:
[tex]-29.5-\frac{38}{15}x[/tex]
Step-by-step explanation:
First, we must expand out the -5.
-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.
x=cos(2t), y=sin(2t) find a rectangular coordinate equation for the curve by eliminating the parameter
Answer:
x^2+y^2=1
Step-by-step explanation:
Since cos^2(x)+sin^2(x)=1, x^2+y^2=1
Please help, I’m not sure about this question.
A shopkeeper bought a second-hand car for Rs 1,50,000. He spent Rs 10,000
on its painting and repair and then sold it for Rs 2,00,000. Find his profit or loss.
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Total People=5+7+4=16
Women=7We know
[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]
[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]
Help please so lost!!!!!!!!!!!!
Answer:
hmmmmm please send the pic again
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation. What is the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.
Answer:
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.
This means that [tex]n = 3923, \pi = \frac{3196}{3923} = 0.8147[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307[/tex]
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Which graph shows data that would allow the most accurate prediction for the number of water bottles a vendor sells based on the daily high temperature?
Graph A
Daily High Temperatures and Bottled Water Sales
On a graph, points are scattered all over the graph.
Graph B
Daily High Temperatures and Bottled Water Sales
On a graph, points are scattered all over the graph.
Graph C
Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Graph D
Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and increase.
PLS HELP ILL GIVE BRAINLIEST FAST
9514 1404 393
Answer:
Graph C: Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Step-by-step explanation:
Apparently, Graph C shows data with the greatest degree of correlation. This suggests that any model of the data is likely to have less error than if the data were less well correlated.
Answer:
Graph C: Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Step-by-step explanation:
A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280πcm3. Find the radius of the can if the height is 16cm16cm. Keep your answers in simplified radical form.
Answer:
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Radius of the can:
The radius of the can is given by:
[tex]r^2 = \frac{V}{h\pi}[/tex]
In which V is the volume and h is the height.
In this question:
[tex]V = 1280\pi, h = 16[/tex]
Thus
[tex]r^2 = \frac{V}{h\pi}[/tex]
[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]
[tex]r^2 = 80[/tex]
[tex]r = \sqrt{80}[/tex]
[tex]r = \sqrt{5*16}[/tex]
[tex]r = \sqrt{5}\sqrt{16}[/tex]
[tex]r = 4\sqrt{5}[/tex]
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Write an equation of the line through each pair of points in slope-intercept form.
a(– 3,–2) and (–3,4)
b(3,2)and (–4,–5)
Answer and I will give you brainiliest
Answer:
see below
Step-by-step explanation:
a) (– 3, –2) and (–3, 4)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(4 - (-2) / (-3 - (-3))
Simplify the parentheses.
= (4 + 2) / (-3 + 3)
Simplify the fraction.
(6) / (0)
= undefined
If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.
In this case, the x-coordinate for both points is -3.
Therefore, your equation is x = -3.
b) (3, 2) and (–4, –5)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-5 - 2) / (-4 - 3)
Simplify the parentheses.
= (-7) / (-7)
Simplify the fraction.
-7/-7
= 1
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = 1x + b or y = x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.
2 = 1(3) + b
To find b, multiply the slope and the input of x(3)
2 = 3 + b
Now, subtract 3 from both sides to isolate b.
-1 = b
Plug this into your standard equation.
y = x - 1
This is your equation.
Check this by plugging in the other point you have not checked yet (-4, -5).
y = 1x - 1
-5 = 1(-4) - 1
-5 = -4 - 1
-5 = -5
Your equation is correct.
Hope this helps!
what is 32⋅(12)x+1=2x−14?
Answer:
[tex]x=-\frac{15}{382}[/tex]
Step-by-step explanation:
32 × 12x + 1 = 2x - 14
384x + 1 = 2x - 14
384x + 1 - 1 = 2x - 14 - 1
384x = 2x - 15
384x - 2x = 2x - 2x - 15
382x = - 15
382x ÷ 382 = - 15 ÷ 382
[tex]x=-\frac{15}{382}[/tex]
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2630. Assume the standard deviation is$500 . A real estate firm samples 100 apartments. Use the TI-84 Plus calculator.a) What is the probability that the sample mean rent is greater than $27007?b) What is the probability that the sample mean rent is between $2450 and $2550? c) Find the 25th percentile of the sample mean. d) Would it be unusual if the sample mean were greater than $26457?e) Do you think it would be unusual for an individual to have a rent greater than $2645? Explain. Assume the variable is normally distributed.
Answer:
a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) The 25th percentile of the sample mean is of $2596.
d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
If |Z|>2, the measure X is considered unusual.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.
This means that [tex]\mu = 2630, \sigma = 500[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]
a) What is the probability that the sample mean rent is greater than $2700?
This is the 1 subtracted by the p-value of Z when X = 2700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2700 - 2630}{50}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value 0.9192
1 - 0.9192 = 0.0808
0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) What is the probability that the sample mean rent is between $2450 and $2550?
This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.
X = 2550
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2550 - 2630}{50}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value 0.0548
X = 2450
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2450 - 2630}{50}[/tex]
[tex]Z = -3.6[/tex]
[tex]Z = -3.6[/tex] has a p-value 0.0002
0.0548 - 0.0002 = 0.0546.
0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) Find the 25th percentile of the sample mean.
This is X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-0.675 = \frac{X - 2630}{50}[/tex]
[tex]X - 2630 = -0.675*50[/tex]
[tex]X = 2596[/tex]
The 25th percentile of the sample mean is of $2596.
Question d and e)
We have to find the z-score when X = 2645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2645 - 2630}{50}[/tex]
[tex]Z = 0.3[/tex]
|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
URGENT 100 POINTS AND BRAINIEST
Question 9 (Essay Worth 10 points)
(04.01, 04.02 HC)
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Part B: How much time does Ted spend practicing the breaststroke every day? Show your work. (3 points)
Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke if he practices for a total of exactly 50 minutes and practices the breaststroke for 20 minutes longer than he practices the butterfly stroke? Explain your reasoning. (2 points)
Answer:
Part A:
x + y = 50
y = x + 20
Part B:
Ted spends 35 minutes practicing the breaststroke every day.
Part C: It is not possible, as 45 + 65 isn't 50.
Step-by-step explanation:
How do i solve this quesiton 6(x − 2) > 15
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]
Flying with a tailwind, a flight crew flew 500 km in 4 hours. Flying against the tailwind, the crew flew 468 km in 4 hours. Find the speed of the plane in calm air and the speed of the wind, both in km per hour.
Answer:
spped of the plane in calm air=121 km/h
speed of the wind= 4km/h
Step-by-step explanation:
Let say V the speed of the plane in calm air
and v the speed of the wind
Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4
Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4
We divide the 2 equations by 4 and then add the 2 results equations:
(500+468)/4=2V ==> V=121 (km/h)
We replace that value in the first equation:
V+v=500/4=125
v=125-121=4 (km/h)
1/2 + 4 5/8 please help
Answer:
[tex]5 \frac{1}{8}[/tex]
Step-by-step explanation:
Remember that [tex]\frac{1}{2} = \frac{4}{8}[/tex], so we want to find [tex]\frac{4}{8} + 4 + \frac{5}{8} = 4 + \frac{9}{8}[/tex]. However, this is not in it's simplest form because [tex]\frac{9}{8}[/tex] should be [tex]1 \frac{1}{8}[/tex]. Therefore, the final answer is [tex]4+1+\frac{1}{8} = 5 \frac{1}{8}[/tex].
Answer:
5 1/8 correct answer to question
In a certain town, 22% of voters favor the construction of a new hospital. For groups of 21 voters, find the variance for the number who did not favor the new hospital.
a. 1.9 voters
b. 4.6 voters
c. none of the given answers is correct
d. 3.6 voters
e. 13 voters
Answer:
Variance = 3.6 voteres
Step-by-step explanation:
Probability of favour voters, P = 0.22
Total number of voters, n = 21
The probability of voters who are in not favour of new hospital construction = 1 - P
The probability of voters who are in not favour of new hospital construction = 1 - 0.22
The probability of voters who are in not favour of new hospital construction, P* = 0.78
Variance = n x p* x (1 - p*)
Variance = 21 x 0.78 x 0.22
Variance = 3.6 voters
Clear parentheses by applying the distributive property.
-(-4s + 9t + 7)
Answer:
4s-9t-7
Step-by-step explanation:
multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same
Write an equation for a line containing (–2,8) that is perpendicular to the line containing the points (3,–4)and (–7,1).
Answer and I will give you brainiliest
Answer:
y = 2x + 12
Step-by-step explanation:
the formula for a line is typically
y = ax + b
a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).
b is the offset of the line in y direction (for x=0).
we have the points (3, -4) and (-7, 1).
to get the slope of the line let's wander from left to right (x direction).
to go from -7 to 3 x changes by 10 units.
at the same time y changes from 1 to -4, so it decreases by 5 units.
so, the slope is -5/10 = -1/2
and the line equation looks like
y = -1/2 x + b
to get b we simply use a point like (3, -4)
-4 = -1/2 × 3 + b
-4 = -3/2 + b
-5/2 = b
so, the full line equation is
y = -1/2 x - 5/2
now, for a perpendicular line the slope exchanges x and y and flips the sign.
in our case this means +2/1 or simply 2.
so, the line equation for the perpendicular line looks like
y = 2x + b
and to get b we use the point we know (-2, 8)
8 = 2×-2 + b
8 = -4 +b
12 = b
so, the full equation for the line is
y = 2x + 12
Answer:
2x-y+12= 0 or y = 2x+12 is the answer
Step-by-step explanation:
slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3
= -5/10
= - 1/2
slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2
Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))
y-8 = 2(x+2)
y- 8 = 2x+4
y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)
Find the value of x. Show your work with proper statements and notation
Answer: x = 14
====================================================
Explanation:
For any triangle, the three inside or interior angles always add to 180
M+N+P = 180
32+64+6x = 180
6x+96 = 180
6x = 180-96
6x = 84
x = 84/6
x = 14
6/5 times 17/18 in lowest terms
Answer:
17/15
Step-by-step explanation:
6/5 * 17/18
1/5 * 17/3
17/15
Denver's elevation is 5280 feet above sea level. Death Valley is -282 feet. Is Death Valley located above sea level or below sea level???
(plz answer, due date is semtemper)
9514 1404 393
Answer:
below
Step-by-step explanation:
When signed numbers are used to represent elevation with respect to sea level, positive signs are used for values above sea level, and negative signs are used for values below sea level. The given elevation of Death Valley indicates it is 282 feet below sea level.
My class consists of 8 men and 7 women. I want to pick a group of 6 people for research.
Write each answer using fraction as needed.
a. In how many different ways can I pick this group?
b. What is the probability of having exactly 3 men in the group?
c. What is the probability of all the selected people in group are women?
d. What is the probability of having at least one man in the group?
Answer:
a.5005
b.[tex]\frac{1960}{5005}[/tex]
c.1/715
d.714/715
Step-by-step explanation:
We are given that
Total men=8
Total women=7
Total people, n=8+7=15
r=6
a.
Combination formula:
Selection of r out of n people by total number of ways
[tex]nC_r[/tex]
Using the formula
We have n=15
r=6
Total number of ways=[tex]15C_6[/tex]
Total number of ways=[tex]\frac{15!}{6!9!}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
Total number of ways=[tex]\frac{15\times 14\times 13\times 12\times 11\times 10\times 9!}{6\times 5\times 4\times 3\times 2\times 1\times 9!}[/tex]
Total number of ways=5005
b. The probability of having exactly 3 men in the group
=[tex]\frac{8C_3\times 7C_3}{15C_6}[/tex]
Using the formula
Probability,[tex]P(E)=\frac{favorable\;cases}{Total\;number\;of\;cases}[/tex]
The probability of having exactly 3 men in the group=[tex]\frac{\frac{8!}{3!5!}\times \frac{7!}{3!4!}}{5005}[/tex]
=[tex]\frac{\frac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\times \frac{ 7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}}{5005}[/tex]
=[tex]\frac{56\times 35}{5005}[/tex]
The probability of having exactly 3 men in the group
=[tex]\frac{1960}{5005}[/tex]
c. The probability of all the selected people in the group are women
=[tex]\frac{8C_0\times 7C_6}{5005}[/tex]
The probability of all the selected people in the group are women
[tex]=\frac{\frac{8!}{0!8!}\times \frac{7\times 6!}{6!1!}}{5005}[/tex]
The probability of all the selected people in the group are women
[tex]=\frac{7}{5005}=\frac{1}{715}[/tex]
d. The probability of having at least one man in the group
=1- probability of all the selected people in group are women
The probability of having at least one man in the group
[tex]=1-\frac{1}{715}[/tex]
[tex]=\frac{715-1}{715}[/tex]
[tex]=\frac{714}{715}[/tex]
The probability of having at least one man in the group [tex]=\frac{714}{715}[/tex]
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5. Calculate the probability of getting at least 4 calls between eight and nine in the morning.
Answer:
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Step-by-step explanation:
We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.
This means that [tex]\mu = 5[/tex]
Calculate the probability of getting at least 4 calls between eight and nine in the morning.
This is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]
[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]
[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]
[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
What is the simplified form of the following expression?
Answer:
-( cube root of 2x)-6(cube root of x)
Please help , write your answer I will be giving 10 points
Answer:
yes it represents the graph accurately
Please Help me and don't report this
8 < x < 8.5 is your answer
other sides has to always be less than the hypotenuse
9514 1404 393
Answer:
0.5 < x < 16.5
Step-by-step explanation:
The sum of the two shortest sides of a triangle must always exceed the length of the longest side.
If x and 8.0 are the short sides, then ...
x + 8.0 > 8.5
x > 0.5
If 8.0 and 8.5 are the short sides, then ...
8.0 +8.5 > x
16.5 > x
So, for the given triangle to exist, we must have ...
0.5 < x < 16.5
_____
Additional comment
You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.
Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES
Answer:
A
Step-by-step explanation:
Slope = term that multiply x
y intercept = the number without a variable
