Question

Suppose that the height of Asian males aged 35–44 in the United States is normally distributed with a standard deviation of 3 in. Jeremy takes a simple random sample of 16 such men and notices that none of them are unusually tall or unusually short. He then calculates the average of the sample to be 69 in. and is planning on using this to find a 95% z?confidence interval for the true mean height.

Can Jeremy use this information to find the z?confidence interval? Complete the following sentences.

The population distribution is_________________ (Options: Irrelevant, unknown, normal , skewed)

The sample______________ (Options: size is irrelevant, size is large enough, contains one or more outliers)

and the population standard deviation is _________________(options: irrelevant, unknown, too big, too small, known)

Therefore,___________(Options, yes all the requirements are met, or no, not all the requirement are met)

Answer 1

Jeremy can indeed use the information to find a 95% z-confidence interval for the true mean height, as the population distribution is normal, the sample size is adequate, and the population standard deviation is known.

Step-by-step explanation:

The population distribution is normal. This is because the question states that the height of Asian males aged 35–44 in the United States is normally distributed, and also given that the sample does not contain any unusually tall or short individuals, suggests that this assumption is valid. The sample size is large enough for the purposes of creating a confidence interval, especially because we are dealing with a sample size of 16 and a normal distribution. Finally, the population standard deviation is known, as the question specifies that it is 3 inches.

Therefore, yes all the requirements are met for Jeremy to use this information to find a 95% z-confidence interval for the true mean height.