1) The average age of CEO's is 56 years. Assume the variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a randomly selected CEO will satisfy each condition:
a) be less than 50 years old
b) be more than 57.5 years old
c) be between 49 and 67 years old.
2) The average charitable contribution deduction on federal tax returns for the year 2007 was $625. Suppose that the distribution of contributions is normal with a standard deviation of $100. Find the limits for the middle 60% of contributions.
3) In a normal distribution, find when is 6 and 3.75% of the area lies to the left of 85.
4) The average teacher's salary in timbucktoo is $29,863. Assume a normal distribution with a standard deviation of $5000.
a) What is the probability that a randomly selected teacher's salary is greater than $32,500?
b) For a sample of 70 teachers', what is the probability that the sample mean will be greater than $32,500?
c) Explain why your answers to parts a) and b) are different.