You are the Director of a local youth services office and the Board has asked you about
Question: Question 3: You are the Director of a local youth services office and the Board has asked you about the average age of the individuals who utilize the office.
(a) Suppose the age distribution of the individuals in the population of clients is well-approximated by a normal distribution with a mean of 20 yrs and a standard deviation of 5 yrs. What proportion of the individuals in the client population are 24.2 years of age or older?
(b) Still assuming that the age distribution of the client population is well-approximated by the normal distribution, calculate the age that represents the 90th percentile of ages in the client population.
(c) One morning you stop the first person who comes into the office and ask her if she is older than 24.2 years old. She says “yes.” Still assuming that the age distribution of the client population is well-approximated by the normal distribution, calculate the probability that she is older than 30 years old.
(d) Using the calculations you made in part (a), calculate the probability that if you were to
take a simple random sample of 8 clients, four or fewer of the clients in the sample would be 24.2 years of age or older.
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