Question

(a) Assume that the population of human body temperatures has a mean of 98∘F   as is commonly believed. Also assume that the population standard deviation is 0.62∘F. If a sample of 100 people are randomly selected, find the probability of getting a sample mean of  98.2∘F or higher? (3pts)

(b) The state of New South Wales has an unemployment rate of 5%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 500 people showed that 20 were unemployed.

1. If the true unemployment rate is 5%, describe the sampling distribution of the sample proportion of unemployed people? (1 pt)
2. Find the probability that the sample unemployment rate is at most 4%. (2 pts)
3. Assume the population proportion p is unknown. Based on the most recent sample, find the probability that the sample proportion will lie within 0.005 of the true proportion pof people who are unemployed. (4 pts)

Answer 1