The diameters of grapefruits in a certain orchard are normally distributed ...

4. Assume that the population of heights of female college students is approximately normally distributed with mean m of 68.66 inches and standard deviation s of 5.13 inches. A random sample of 67 heights is obtained. Show all work. (A) Find the mean and standard error of the distribution (B) Find P(xbar > 69.75) 

5. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.97 inches and a standard deviation of 0.69 inches. Show all work. (A) What percentage of the grapefruits in this orchard is larger than 6.01 inches? (B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 6.01 inches? 

6. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 5.31, how large a sample is needed to get the desired information to be accurate within 0.63 decibels?