IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15.
(a) Find the IQ scores that represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
(c) Find the IQ score for the top 5%.

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

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.

Answer:

17/15

Step-by-step explanation:

6/5 * 17/18

1/5 * 17/3

17/15

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]

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.

Answer:

-( cube root of 2x)-6(cube root of x)

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)

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

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.

Answer:

A

Step-by-step explanation:

Slope = term that multiply x

y intercept = the number without a variable

Total People=5+7+4=16

We know

[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]

[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]

Answer:

x^2+y^2=1

Step-by-step explanation:

Since cos^2(x)+sin^2(x)=1, x^2+y^2=1

Answer:

18.65

Step-by-step explanation:

1/4+2/5+18=18.65

18.65

hope it helps you good luck

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

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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:

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]

Answer:

hmmmmm please send the pic again

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).

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]

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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.

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

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!

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.

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)

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

Answer:

yes it represents the graph accurately

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:

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]