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Chapter 7: Q. 2.3 (page 488)

In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is

a. left-skewed with mean 122 and standard deviation 0.35.

b. exactly Normal with mean 122 and standard deviation 5.

c. exactly Normal with mean 122 and standard deviation 0.35.

d. approximately Normal with mean 122 and standard deviation 5.

e. approximately Normal with mean 122 and standard deviation 0.35.

Short Answer

Expert verified

(e) Approximately normal with mean is 122 and standard deviation is 0.35

Step by step solution

01

Given Information 

The mean is 渭=122

Standard deviation is 蟽=5

The number of persons n=200

The following concept was used:

蟽x炉=蟽n

02

Explanation for correct option 

The sample size is larger than 33.

By Know that the sampling distribution of the central limit theorem sample meanx炉is concerned with the ordinary.

渭x炉=渭=122蟽x炉=蟽n=5200=0.35

As a result, the sample mean's sampling distribution is close to normal, with a mean of 122 and a standard deviation of 0.35.

03

Explanation for incorrect option 

a. left-skewed with not provided mean 122 and standard deviation 0.35

b. exactly Normal with not provided mean 122 and standard deviation 5

c. exactly Normal with not provided mean 122 and standard deviation 0.35

d. approximately Normal with not provide mean 122 and standard deviation 5

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Most popular questions from this chapter

Finch beaks One dimension of bird beaks is "depth"-the height of the beak where it arises from the bird's head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be Normally distributed with mean 渭=9.5鈥�millimeters(mm)and standard deviation 蟽=1.0mm.

a. Choose an SRS of 5 Medium Ground Finches from this population. Describe the sampling distribution of x炉.

b. Find the probability that x炉estimates 渭within 卤0.5mm. (This is the probability that x炉takes a value between 9 and 10 mm.

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refer to the following graph. Here is a dotplot of the adult literacy rates in 177 countries in a recent year, according to the United Nations. For example, the lowest literacy rate was 23.6 %, in the African country of Burkina Faso. Mali had the next lowest literacy rate at 24.0 %.

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b. clearly skewed to the left.

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a. Less than 10 minutes

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Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

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A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x炉. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x炉will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

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