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Chapter 7: Q. 30 (page 457)

The math department at a small school has 5teachers. The ages of these teachers are 23,34,37,42,58. Suppose you select a random sample of 4teachers and calculate the sample minimum age. Which of the following shows the sampling distribution of the sample minimum age?

a.

b.

c.

d.

e. None of these

Short Answer

Expert verified

The correct option (c) i.e.

Step by step solution

01

Given information

We need to find the correct option showing the sampling distribution of the sample minimum age.

02

Explanation

We know that

The smallest age out of the four ages in the sample are

Sample of size fourSample minimum
23,34,37,42
23
23,34,37,58
23
23,34,42,58
23
23,37,42,58
23
34,37,42,58
34

We then remark that the sample minimum sampling distribution should include 4dots at 23and 1dot at 34. (since there are 4samples with sample minimum 23and one sample with sample minimum 34).

Therefore, the correct option is (c) i.e.

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Most popular questions from this chapter

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value (\(500,\)100,\(25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket:

Which of the following are the mean and standard deviation, respectively, of the winnings?

a. \)15.00,\(2900.00

b. \)15.00,\(53.85

c. \)15.00,\(26.93

d. \)156.25,\(53.85

e. \)156.25,$26.93

A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.

a. Without doing any calculations, explain which event is more likely:

  • randomly selecting 1 car entering this interchange during rush hour and finding 2 or more people in the car
  • randomly selecting 35 cars entering this interchange during rush hour and finding an average of 2 or more people in the cars

b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).

c. Calculate the probability of the second event in part (a).

Sample minimums List all 6possible SRSS of size n=2, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased estimator of the population minimum? Explain your answer.

COLORAGE
RED1
WHITE5
SILVER8
RED20

Healthy Living From a large group of people who signed a card saying they intended to quit smoking, 1000 people were selected at random. It turned out that 210(21%) of these individuals had not smoked over the past 6 months.

The number of unbroken charcoal briquets in a 20-pound bag filled at the factory follows a Normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. The company expects that a certain number of the bags will be underfilled, so the company will replace for free the 5%of bags that have too few briquets. What is

the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free?

a. 404

b. 411

c. 418

d. 425

e. 448
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