1.Suppose 3% of all Ray-Bans have a manufacturing defect. Is a sample size of 54 sufficient to guarantee that the sampling distribution of the proportion will be normally distributed?
a. Yes, as the sample size is at least 30, the central limit theorem says that the sample is large enough for the sampling distribution of the proportion to be normally distributed.
b. The central limit theory says that real world data is close enough to being normally distributed to assume that the sampling distribution is also normally distributed.
c. Yes, as np and n(1-p) are at least equal to five.
d. No, either np or n(1-p) are less than five.
e. There is not enough information to answer this question.
2. Suppose a population is not normally distributed and not symmetric. If the sample size is 25, what does the central limit theory say about the sampling distribution of the mean?
a. The sample size is not large enough to assume the sampling distribution of the mean is normally distributed.
b. We can never assume the sampling distribution of the mean is normally distributed if the population data is not normally distributed.
c. The sample size is large enough to assume the sampling distribution of the mean is normally distributed.
d. The sampling distribution of the mean is normally distributed since the magnitude of the standard deviation is less than the mean.
e. The central limit theory says that real world data is close enough to being normally distributed to assume that the sampling distribution is also normally distributed.