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Chapter 7: Q.10 (page 460)

Suppose that you are a student aide in the library and agree to be paid according to the 鈥渞andom pay鈥� system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is \(80. If it comes up tails, your pay for the week is \)40. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x. The shape of the sampling distribution of xwill be

(a) Normal.

(b) approximately Normal

(c) right-skewed

(d) left-skewed.

(e) symmetric but not Normal.

Short Answer

Expert verified

The Correct answer is (e)

Step by step solution

01

Given Information

Payment for the week if the coin comes up heads=$80

Payment for the week if the coin comes up tails=$40

Number of weeks of work=100

Number of weeks for SRS = 2

02

Explanation

Given the number of the week for SRS is 2.

This means the average amount could be $40for two weeks,$80for two weeks, or $60( $40for one week and $80for the other week).

It is seen that getting $60is twice likely because on the first week $40can be obtained and $80on the second week or vice versa.

Thus, the distribution will be symmetric $60and it will also be normal.

Hence, the correct answer is (e).

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Most popular questions from this chapter

In the language of government statistics, you are 鈥渋n the labor force鈥� if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged 25years and over in a recent year. The table entries are counted by thousands of people.

Unemployment (5.1) What is the probability that a randomly chosen person 25 years of age or older is in the labor force? Show your work.

The correlation between the age and height of children under the age of 12is found to ber=0.60. Suppose we use the agex of a child to predict the height y of the child. What can we conclude?
(a) The height is generally60% of a child鈥檚 weight.
(b) About60% of the time, age will accurately predict height.
(c) The fraction of the variation in heights explained by the least-squares regression line of yon xis0.36.
(d) The least-squares regression line of yon xhas a slope of0.6.
(e) Thirty-six percent of the time, the least-squares regression line accurately predicts height.

The standard deviation of the average scores you get should be close to

(a) 114.

(b) 114/100=1.14.

(c) 114/100=11.4.

(d) 1.

(e) none of these.

Suppose we roll a fair die four times. The probability that a 6occurs on exactly one of the rolls is

(a) 4163561

(b) 4161563

(c) 6161563

(d) 163561

(e)161563

Songs on an iPod David's iPod has about 10000songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225seconds and a standard deviation of 60seconds. How many songs would you need to sample if you wanted the standard deviation of the sampling distribution of x炉to be30seconds? justiify your answer.
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