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Chapter 7: Q.9 (page 460)

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is 16.05ounces with a standard deviation of 0.1ounces. Assume that the machine is working properly. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95%of the observations should occur in which interval?

(a) 16.05to 16.15ounces

(b) 0.30to 0.30ounces

(c) 15.95to16.15 ounces

(d) 15.90to 16.20ounces

(e) None of the above

Short Answer

Expert verified

The correct answer is (e)

Step by step solution

01

Given Information

Amount of bottles of shampoo to fill the mach谋ne =16ounces

Mean amount of shampoo =16.05ounces

Standard deviation =0.1ounce

Number of randomly selected bottles=4

02

Explanation

Consider that nrepresents the number of randomly selected bottles that is, n=4;蟽represents the standard deviation that is 蟽=0.1, and 渭denotes the mean that is, 渭=16.05.

In the case of a Normal distribution, it is known that 95%the observations lie within 2standard deviations of the mean. But it is not given that the population distribution is normal so the central limit theorem cannot be applied.

Hence, the correct answer is (e).

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Most popular questions from this chapter

On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20ounces of iced tea. Quality control inspectors sampled50bottles at random from the day鈥檚 production. These bottles contained an average of 20ounces of iced tea.

Which of the following statements about the sampling distribution of the sample mean is incorrect? (a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

(c) The sample mean is an unbiased estimator of the true population mean.

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean

Dem bones (2.2) Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD score that is 2.5standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and gender roughly follow a Normal distribution.

(a) What percent of healthy young adults have osteoporosis by the WHO criterion?

(b) Women aged 70to79 are, of course, not young adults. The mean BMD in this age group is about 2 on the standard scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population has osteoporosis?

If we take a simple random sample of size n=500from a population of size 5,000,000, the variability of our estimate will be

(a) much less than the variability for a sample of size n=500 from a population of size 50,000,000.

(b) slightly less than the variability for a sample of size n=500from a population of size 50,000,000.

(c) about the same as the variability for a sample of size n=500from a population of size 50,000,000.

(d) slightly greater than the variability for a sample of size n=500from a population of size 50,000,000.

(e) much greater than the variability for a sample of size n=500 from a population of size 50,000,000.

A researcher initially plans to take anSRS of size n from a population that has a mean of 80 and a standard deviation of 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by

(a) 2.

(b)12 .

(c) 2.

(d) 12.

(e)12n
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