1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivanshal [37]
3 years ago
10

Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length

follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 21 ads produced by Majesty.a. What can we say about the shape of the distribution of the sample mean time?b. What is the standard error of the mean time? (Round your answer to 2 decimal places)c. What percent of the sample means will be greater than 27.05 seconds?d. What percent of the sample means will be greater than 25.05 seconds?e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"
Mathematics
1 answer:
Paladinen [302]3 years ago
8 0

Answer:

a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b) s = 0.44

c) 0.84% of the sample means will be greater than 27.05 seconds

d) 98.46% of the sample means will be greater than 25.05 seconds

e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

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 normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation(also called standard error) s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 26, \sigma = 2, n = 21, s = \frac{2}{\sqrt{21}} = 0.44

a. What can we say about the shape of the distribution of the sample mean time?

By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b. What is the standard error of the mean time? (Round your answer to 2 decimal places)

s = \frac{2}{\sqrt{21}} = 0.44

c. What percent of the sample means will be greater than 27.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 27.05. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{27.05 - 26}{0.44}

Z = 2.39

Z = 2.39 has a pvalue of 0.9916

1 - 0.9916 = 0.0084

0.84% of the sample means will be greater than 27.05 seconds

d. What percent of the sample means will be greater than 25.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 25.05. So

Z = \frac{X - \mu}{s}

Z = \frac{25.05 - 26}{0.44}

Z = -2.16

Z = -2.16 has a pvalue of 0.0154

1 - 0.0154 = 0.9846

98.46% of the sample means will be greater than 25.05 seconds

e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"

This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.

X = 27.05

Z = \frac{X - \mu}{s}

Z = \frac{27.05 - 26}{0.44}

Z = 2.39

Z = 2.39 has a pvalue of 0.9916

X = 25.05

Z = \frac{X - \mu}{s}

Z = \frac{25.05 - 26}{0.44}

Z = -2.16

Z = -2.16 has a pvalue of 0.0154

0.9916 - 0.0154 = 0.9762

97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

You might be interested in
Need help on this worksheet
andre [41]

Answer:

1. $1650

2. $1415.52

3. $5540

4. No

5. 145

6. No

Step-by-step explanation:

1. 2230 - 580

2. 157.28 x 9

3. 6630 - 1090

4.

5. 725 - 580

Hope this helps!

8 0
3 years ago
If the point (-1/2, y) lies on the line whose equation is 2x - 3y = 6, what is the value of y?
salantis [7]
Plug in the known x value

2(-1/2)-3y=6
-1-3y=6
-3y=7
y=-7/3

Final answer: -7/3
4 0
3 years ago
when n basketball uniforms are purchased , the cost , C , of each uniforms is given by the equation C=40n+260/n. if the cost of
Luda [366]

Hello!

As you can see, C is the cost of each uniform. This would give us the equation below, if each uniform was $60.

60=40n+260/n

Let's multiply both sides by n.

60n=40n+260

Now, let's subtract 40n from both sides.

20n=260

We divide both sides by 20.

n=13

Therefore, 13 uniforms were purchased.

I hope this helps!

7 0
3 years ago
Read 2 more answers
Write this statement as a conditional statement in the form “if p, then q.”
ss7ja [257]

Answer:

if the measure of an angle is 90°, then the angle is a right angle.

Step-by-step explanation:

p=the measure of an angle is 90°

q=the angle is a right angle

p is the hypothesis of the conditional statement

q is the conclusion of the conditional statement

5 0
2 years ago
You can buy an 8-pack of paper towels for $8.40 or a 12-pack for $12.36. Which is the better buy?
mixas84 [53]

Answer: 12 pack

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Two numbers have a sum of 42. The larger number is 6 more than the smaller. Find the nunbers
    11·1 answer
  • Is It Safer To Drive Or Get On A Plane?
    9·2 answers
  • Write an equation of a line that passes through the given point and has slope m<br> (3,4) m=1/2
    11·2 answers
  • During his summer vacation, Alex spent 6 minutes riding his bike for every minute he spent watching television. If he rode his b
    7·1 answer
  • What is the relationship between 5 in these two numbers 8,523 and 9,852
    5·1 answer
  • If the 1st and 10th terms of geometric sequence are 4 and 100. Fine the nth term of the sequence
    10·1 answer
  • Write and simplify an expression to represent the perimeter of the triangle shown. Then find the value of x if the perimeter is
    10·1 answer
  • A doctor takes an uber from the airport to a hotel. The uber driver charges an $2.50 initial charge plus $2.65 per mile? Which e
    8·1 answer
  • Which is bigger -7/11 or -2/3
    8·1 answer
  • To test if x is a good predictor of y in Simple Linear Regression we need to determine whether:
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!