Question

A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution? Select all that apply. A. The researcher collects more than 30 samples. B. If the population of statistics students has a normal distribution. c. If the population of grade-point averages has a normal distribution, D. The sample has more than grade-point averages. Click to select your answer(s) and then click Check Answer. ? All parts showing Clear All Check Answer If np25 and nq 25, estimate P(at least 5) with n= 13 and p=0.5 by using normal distribution as an approximation to the binomial distribution; if np<5 or ng <5, then state that the normal approximation is not suitable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A P(at least 5) = (Round to three decimal places as needed.) OB. The normal distribution cannot be used.

Answer 1

The sample mean can be treated as a value from a population having a normal distribution if the researcher collects more than 30 samples and if either the population of statistics students or the population of grade-point averages has a normal distribution.

Step-by-step explanation:

In order for the sample mean to be treated as a value from a population having a normal distribution, the conditions that need to be met are:

1. The researcher collects more than 30 samples.
2. The population of statistics students has a normal distribution.
3. The population of grade-point averages has a normal distribution.

Answer 2

The conditions for the sample mean to be treated as a value from a normal distribution.

Step-by-step explanation:

In order for the sample mean to be treated as a value from a population with a normal distribution, the following conditions need to be met:

• The population of grade-point averages has a normal distribution
• The sample size is greater than or equal to 30

Only conditions B and A are correct. The population of statistics students having a normal distribution and the sample size being larger than 30 are both necessary for the sample mean to approximate a normal distribution.