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Chapter 7: Q. T7.4 (page 486)

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

a. sample size is reasonably large (for any population).

b. population is Normally distributed (for any sample size).

c. population is Normally distributed and the sample size is reasonably large.

d. population is Normally distributed and the population standard deviation is known (for any sample size).

e. population size is reasonably large (whether the population distribution is known or not).

Short Answer

Expert verified

(a) The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the sample size is reasonably large (for any population).

Step by step solution

01

Given Information

The central limit theorem is significant in statistics because it allows us to find probabilities involving the sample mean using a Normal distribution.

02

Explanation for correct option

According to the central limit theorem, if the sample size is big, the sampling distribution of the sample mean x炉is approximately normal.

As a result, the best solution is (a)

03

 Step 3: Explanation for incorrect option

b. population is Normally distributed (for any sample size) is not the answer.

c. population is Normally distributed and the sample size is reasonably large is not the answer.

d. population is Normally distributed and the population standard deviation is known (for any sample size) is not the answer.

e. population size is reasonably large (whether the population distribution is known or not) is not the answer.

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The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is 50\( and the standard deviation is 20\). The distribution is not Normal: many households pay a low rate as part of a bundle with phone or television service, but some pay much more for Internet only or for faster connections. 11 A sample survey asks an SRS of 50 households with Internet access how much they pay. Let x-x炉be the mean amount paid.

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