Answer:
0.6121 = 61.21% probability that the sample average amount of time taken on each day is at most 11 min.
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.
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.
Normal distribution with mean value 10 min and standard deviation 3 min.
This means that [tex]\mu = 10, \sigma = 3[/tex]
First day:
5 individuals, so [tex]n = 5, s = \frac{3}{\sqrt{5}}[/tex]
The probability is the p-value of Z when X = 11. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 10}{\frac{3}{\sqrt{5}}}[/tex]
[tex]Z = 0.745[/tex]
[tex]Z = 0.745[/tex] has a p-value of 0.7719.
Second day:
6 individuals, so [tex]n = 6, s = \frac{3}{\sqrt{6}}[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 10}{\frac{3}{\sqrt{6}}}[/tex]
[tex]Z = 0.817[/tex]
[tex]Z = 0.817[/tex] has a p-value of 0.793.
What is the probability that the sample average amount of time taken on each day is at most 11 min?
Each day is independent of other days, so we multiply the probabilities.
0.7719*0.793 = 0.6121
0.6121 = 61.21% probability that the sample average amount of time taken on each day is at most 11 min.
When I add 45 to a certain number and divide the sum by 2, the result is the same as 5 times the number. What is the number?
Answer:
5
Step-by-step explanation:
(45 + x) / 2
add 45 to a certain number and divide the sum by 2
= 5 × x
is 5 times the number
(45 + x)/2 = 5x
45 + x = 10x
45 = 9x
x = 5
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
A store has x packages of 4 markers and y packages of 12 markers. The store has a total of 192 markers in
stock. If there are 21 packages of 4 markers in the store, how many packages of 12 markers are there?
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14) Students at East Central High School earned $246
selling pennants. They want to make $3810 for a
club trip. What percent of their goal has been
reached? Round to the nearest tenth of a percent,
if necessary.
Answer:
6.46%
Step-by-step explanation:
246 ÷ 3810 × 100% = 6.46%
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.
Answer:
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
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 590 hours, standard deviation of 25 hours.
This means that [tex]\mu = 590, \sigma = 25[/tex]
Find the probability of a bulb lasting for at most 622 hours.
This is the p-value of Z when X = 622.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{622 - 590}{25}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997.
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
Jim took a loan of R30 000.00 for 18 months at a simple interest rate of 12.5% per year. Determine the amount that Jim
will pay in 18 months.
Answer:
R35625
Step-by-step explanation:
(R30,000×.125×18/12)+R30000
=R35625
75% increase followed by 50% decrease is it greater than to original
Answer:
Set original amount = xAfter a 75% increase, it would become
x + 75%x = x + 0.75x = x(1 + 0.75) = 1.75x
After a 50% decrease, it would become
1.75x - 50%(1.75x) = 1.75x - 0.5(1.75x) = 1.75x - 0.875x = 0.875x = [tex]\frac{7}{8} x[/tex]
Because [tex]\frac{7}{8} x[/tex] is less than x, the new amount would be less than the original.
Name three different ways a bar graph can be drawn.
A zookeeper published the following stem-and-leaf plot showing the number of lizards at each major zoo in the country:
∣
0
1
2
3
4
5
6
∣
0
6
8
8
8
0
2
6
6
7
8
1
2
6
6
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
00
10
20
30
40
50
60
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
0
0
0
0
1
0
0
6
2
2
8
6
6
8
6
6
8
7
0
0
8
0
Key:
2
∣
0
=
20
2∣0=202, vertical bar, 0, equals, 20 lizards
How many zoos have more than 26 lizards
A physical education class is running a mile. The teacher has set a goal of 12 minutes to complete the mile. Students
receive a score to show how close they are to the target of 12 minutes. For example, if students run the mile in 8
minutes, their scores will be 4. Complete the statements about the students' scores.
Anja ran the mile in Her score is -2.
Issac ran the mile in 13 minutes. His score is
Simon ran the mile in 12 minutes. His score is
Answer:
Isaac is 26
Simon is 24
if 8 is 4 I.e 8 divide by 4 is 2
therefore 1 minute is 2 scores
Isaac :13 x 2=26
(do the same to Simon to get his score)
A 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy
Answers:
First bottle's unit cost = 27 cents per oz
Second bottle's unit cost = 27 cents per oz
Both have the same unit cost.
----------------------------------------
Work Shown:
unit cost = price/(number of ounces)
1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz
2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz
Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.
9+1+10+6×5+9+8×9+8+8+7+6+6+9+6+8+69+85+86+86+97+86+87+86+68
Step-by-step explanation:
hope it will help u
hope it will help u please mark me as brillient...
Answer:
939 is the answer
Step-by-step explanation:
plz Mark me as the brainlist
prove that Sin^6 ϴ-cos^6ϴ=(2Sin^2ϴ-1)(cos^2ϴ+sin^4ϴ) please sove step by step with language it is opt maths question please sove i will mark you the best
Answer:
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The surface area of a cylinder?
Answer:
18. 84 ft² or 18.85 ft² when rounded to the nearest tenth
Step-by-step explanation:
2πrh+2πr²
2× 3.14 × 1 × 2= 12.56
2 × 3.14 × 1² = 6.28
12.56 + 6.28 = 18.84
Have a great day :)
Answer:
18.85 [tex]ft^2\\[/tex]
*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*
Step-by-step explanation:
Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]
Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.
I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.
Radius: 1 Height: 2
Plug numbers into equation:
[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]
I hope that helps!
Cost of Building a Home According to the National Association of Home Builders, the average cost of building a home in the Northeast is per square foot. A random sample of new homes indicated that the mean cost was and the population standard deviation was . Can it be concluded that the mean cost differs from , using the level of significance
Answer:
There isn't sufficient evidence that support the claim that mean cost differs from $117.91
Step-by-step explanation:
Given that :
Population Mean cost, μ = 117.91
Sample size, n = 36
Sample mean, xbar = 122.57
Sample standard deviation, s = 20
The hypothesis :
H0 : μ = 117.91
H0 : μ ≠ 117.91
Using the one sample t test :
Test statistic
(xbar - μ) ÷ s/sqrt(n)
T = (122.57 - 117.91) ÷ 20/sqrt(36)
T = 4.66 / 3.333
T = 1.398
Decision region :
Reject H0 ; If Pvalue < α
α = 0.10
Degree of freedom, df = n - 1 = 36 - 1 = 35
Pvalue(1.398, 35) = 0.1709
Since 0.1709 > 0.10 ; WE fail to reject H0 ; therefore there isn't sufficient evidence that support the claim that mean cost differs from $117.91
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) F(x) = sin(x/2) , [π/2,3π/2]
Answer:
The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem
Step-by-step explanation:
1. The function must be continuous.
Trigonometric functions are continuous.
2. It must be true that f(a) = f(b) = 0
For this case sin(pi) = sin(3pi) = 0
3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0
For this case f(x) = cos(x)
And cos(x) = 0 at x = 3(pi)/2,5(pi)/2
A couple decide to have 5 children what if the probability that they will have at least one girl
Answer:
31/32
Step-by-step explanation:
There are 2^5, or 32 combinations.
There is only 1 combination which is all 5 children are boys.
So the probability that will have at least 1 girl is: 1 - 1/32 = 31/32
If Y / 4 - 12 = 3.5, what is the value of y?
Identify the terminal point for a 45° angle in a unit circle.
O A (231)
O B.
O c.
V2 72
Answer:
D
Step-by-step explanation:
x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D
Find the area of the parallelogram. Show all your work.
Answer:
30m^2
Step-by-step explanation:
area of parallelogram is b×h
Answer:
The area of the parallelogram is 30 square meters.
Step-by-step explanation:
The area of a parallelogram is given by the formula:
A = bh
Where b is base and h is height
The base of the parallelogram is:
6 + 4 = 10 m
The height perpendicular to the base is 3 m
Use the formula A = bh:
A = (10)(3)
= 30
So the area of the paralleogram is 30 m^2
Hope this helps!
w • (-4+ z) = mz + 17
z = ____
solve for z.
ps.. pls help me lol. i need the answer
Answer:
z = (17+4w)/(w-m)
Step-by-step explanation:
w • (-4+ z) = mz + 17
Distribute
-4w +wz = mz+17
Subtract mz from each side
-4w +wz - mz = mz+17-mz
-4w +wz-mz = 17
Add 4w to each side
-4w +4w+wz-mz = 17+4w
wz-mz = 17+4w
Factor out z
z(w-m) = 17+4w
Divide by (w-m)
z(w-m)/(w-m) = (17+4w)/(w-m)
z = (17+4w)/(w-m)
URGENT!!!PLEASE HELP! PLEASE PLEASE!
Choose the number below that fits into the following number sets:
Natural Number
Whole Number
Integer
A. -½
B. 4.9
C. π
D. 6
Answer:
d) 6
Step-by-step explanation:
natural number = +ve numbers, so -1/2 is out
4.9 and π arent whole numbers nor intergers
Can someone please help me solve the equation?
Answer:
(0,0) is the x and y intercept of the function
Step-by-step explanation:
The parabola touches the x and y axis at 0
The x intercept is (0,0) and the y intercept is (0,0)
Answer:
(0, 0) is the x and y intercepts
Step-by-step explanation:
intercepts are where the curve of the equation contacts an axis
The equation is y = x²
fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50 how many miles was the trip to the airport
the trip to the airport was 6.25 miles.
Given that ƒ(x) = 3^x, identify the function g(x) shown in the figure. A) g(x) = −3^-x
B) g(x) = −(1∕3)^x
C) g(x) = 3^−x
D) g(x) = −3^x
Answer:
Option (D)
Step-by-step explanation:
From the graph attached,
Function 'f' is the reflected across x-axis to get the graph function 'g'.
Therefore, by definition of reflection across x-axis,
g(x) = -f(x)
g(x) = [tex]-3^x[/tex]
Option (D) will be the answer.
Please Help me! I will mark brainliest for correct answer!!!
Answer:
y=2/3x+1
Step-by-step explanation:
Given the parent graph h(x) = x, what happens when it is changed to h(x + 9)?
Answer:
If the parent graph is h(x) = x, then h(x+9) would actually be shifting the graph 9 units to the LEFT.
Let me know if this helps!
It takes 12 people 15 hours to complete and certain job.how many hours would it take 18 people, working at the same rate to complete 2/5 of the same job?
Answer:
9 hours
Step-by-step explanation:
12 people take 15 hours to complete one job. First let's ask how long it would take 18 people working at the same rate to complete the same job? We can use proportions to answer this
[tex]\frac{12 people}{15 hours} = \frac{18 people}{x hours}\\x = \frac{18\times15}{12} = 22.5[/tex]
Now we know that one job takes 18 people 22.5 hours, so 2/5 of the job would take
[tex]\frac{18\times15}{12} \times \frac{2}{5} = 9[/tex]
7. Solve -4(6x + 3) = -12(x + 10).
in a children of 700 inmates,25% are living with polio and 30% are girls . if 30% og the girls have polio, how many are the boys without polio
Answer: 378 Boys
Explanation:
Total no. Inmates = 700
Living with polio = 25/100×700
= 175 inmates
Total girls = 30/100×700
= 210 Girls
30% of girls Having polio = 30/100×210
= 63 Girls
Total Boys = 700 - 210
= 490 Boys
Total boys with polio = 175 - 63
= 112 boys
Boys without polio = 490 - 112
= 378 boys
Must click thanks and mark brainliest
