Assume that from years of collecting data we know that the mass of all adult South Africans is normally distributed with a standard deviation of 15. A researcher selects a random sample of South Africans.
a) To estimate the mass of the adult population of South Africans, what information would the researcher require?
b) If the researcher draws a random sample of 250 adult South Africans, what is the standard error of estimate?
c) To ensure that the standard error is no smaller than 0.5, how large would the sample have to be?
d) Let us say that after years of collecting data, the mean mass of the adult South African population is found to be 75 kg.
i) If the researcher selects a random sample of 20 people, what is the probability that their mean mass will be less than 70 kg?
ii) What is the probability that the mean mass of this sample of 20 will fall between a mean mass of 65 kg and a mean mass of 80 kg?
iii) If the researcher draws a sample of 50 people, what is the probability that the mean mass for this sample will be greater than 80 kg?
iv) If the researcher draws a sample of only 10 people, what is the probability that the mean for this sample will be less than 60 kg?