Question

Consider the following variables. For each variable, identify its distribution as either "Exactly Normal," "Approximately Normal," or "Neither" (short for neither Exactly Normal nor Approximately Normal). • Life expectancy in a country is known to follow a left-skewed distribution Suppose we take a random sample of 7 citizens and denote the sample mean life expectancy by X. The distribution of X is Choose... . The weights of bananas follow a Normal distribution Suppose we take a sample of 8 bananas, and denote the sample mean weight by X The dutribution of X is Choose • Run times at a marathon are known to follow a left-skewed distribution Suppose we take a sample of 36 runners, and denote the sample mean run time by X. The distribution of X is Choose In a certain city, it is known that 3.5% of the residents have red hair Suppose we take a sample of 700 residents, and denote the sample proportion of members with red hair by P. The distribution of pis Choose... Albinism is estimated to occur in 0.00588% of all people. Suppose we take a random sample of 500 people, and denote the sample proportion of memb with albinism by p. The distribution of pis Choose

Answer 1

In this problem, we need to find the underlying distribution is exactly normal, approximately normal or neither.

a) here we collect n=7 samples from a positively skewed distribution, then the sample mean will have Neither because of a small sample from the non-normal population.

b) here we collect n=8 samples from a normal distribution, then the sample mean will have Exactly normal because of the normal population.

c) here we collect n=86 samples from a positively skewed distribution, then the sample mean will have approximately normal because of a high sample size.

d) here we collect n=700 samples and a sample proportion being calculated, then the sample proportion will have approximately normal because of high sample size, and law of proportion converges to normality approximately.

e) here we collect n=500 samples and a sample proportion being calculated, then the sample proportion will have approximately normal because of high sample size, and the law of proportion converges to normality approximately.