1. Assume that the population of heights of male college students is approximately normally distributed with meanm of 68 inches and standard deviations of 3.75 inches. A random sampleof 16 heights is obtained. Find the proportion of male college students whose height is greater than 70 inches.

2. The diameters of oranges in a certain orchard are normally distributed with a mean of 5.26 inches and a standard deviation of 0.50 inches.

a. What percentage of the oranges in this orchard have diameters less than 4.5 inches? b. What percentage of the oranges in this orchard is larger than 5.12 inches? c. A random sample of 100 oranges is gathered and the mean diameter obtained was 5.12. If another sample of 100 is taken, what is the probabilitythat its sample mean will be greater than 5.12 inches? Why is the z-score used in answering (a), (b), and (c)?

3. Consider a binomialdistribution with 15 identical trials, and a probability of success of 0.5. a. Find the probability that x = 2 using the binomial tables. Use the normal approximation to find the probability that x = 2

Neat and step-by-step solutions to all the three problems.