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Chapter 7: Q. 73 (page 481)

The distribution of scores on the mathematics part of the SAT exam in a recent year was approximately Normal with mean 515 and standard deviation 114 . Imagine choosing many SRSs of 100 students who took the exam and averaging their SAT Math scores. Which of the following are the mean and standard deviation of the sampling distribution of x-?x炉?

a. Mean =515,SD=114

b. Mean =515,SD=114/100SD=114/100

c. Mean role="math" localid="1654342976765" =515/100,SD=114/100

d. Mean role="math" localid="1654343050312" =515/100,SD=114/100SD=114/10

e. Cannot be determined without knowing the 100 scores.

Short Answer

Expert verified

The value of Mean =515and SD=114100

The correct option is (b)

Step by step solution

01

Given information 

Given,

渭=515蟽=114n=100
02

Explanation for correct option

Calculation:

渭x炉=渭=515蟽x炉=蟽n=114100

Hence, the correct option is (b)

03

Explanation for incorrect option

(a). mean=515,SD=114are not the mean and standard deviation of the sampling distribution of role="math" localid="1654343011275" x-and role="math" localid="1654343023938" x炉

(c). Mean=515/100,SD=114/100are not the mean and standard deviation of the sampling distribution of role="math" localid="1654343077524" x-and role="math" localid="1654343088243" x炉

(d). Mean=515/100,SD=114/100SD=114/10are not the mean and standard deviation of the sampling distribution of x-and x炉

(e). Cannot be determined without knowing the 100 scores is incorrect statement

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Most popular questions from this chapter

Doing homework A school newspaper article claims that 60%of the students at a large high school completed their assigned homework last week. Assume that this claim is true for the 2000students at the school.

a. Make a bar graph of the population distribution.

b. Imagine one possible SRS of size 100from this population. Sketch a bar graph of the distribution of sample data.

Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean 渭=298mland standard deviation 蟽=3ml.

a. What is the probability that a randomly selected bottle contains less than 295ml?

b. What is the probability that the mean contents of six randomly selected bottles is less than 295ml?

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

a.4(16)3(56)14163561b.(16)3(56)1163561c.4(16)1(56)3161563d.(16)1(56)3161563e.6(16)1(56)36161563

Dead battery? A car company claims that the lifetime of its batteries varies from car to car according to a Normal distribution with mean 渭=48months and standard deviation 蟽=8.2months. A consumer organization installs this type of battery in an SRS of 8 cars and calculates x炉=42.2months.

a. Find the probability that the sample mean lifetime is 42.2 months or less if the company's claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average lifetime of its batteries?

Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution ofx-x炉 to be 10 seconds? Justify your answer.
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