1) The undergraduate grade point averages(UGPA) of students taking an admissions test in a recent year can be approximated by a normaldistribution, as shown in the figure.

(a) What is the minimum UGPA that would still place a student in the top 15% ofUGPAs?

(Round to two decimal places asneeded.)

(b) Between what two values does the middle 50% of the UGPAslie?

A normal curve labeled mu = 3.42 and sigma = 0.19 is over a horizontal x-axis labeled Grade point average from 2.84 to 4 in increments of 0.29 and is centered on 3.42.

(Round to two decimal places asneeded.)

2)The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 8 days.

(a) What is the minimum pregnancy length that can be in the top 8% of pregnancylengths?(Round to one decimal place asneeded.)

(b) What is the maximum pregnancy length that can be in the bottom 7% of pregnancylengths?(Round to one decimal place asneeded.)

3)The mean height of women in a country(ages 2029) is 64.3 inches. A random sample of 55 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume =2.63.

The probability that the mean height for the sample is greater than 65 inches is ............?(Round to four decimal places asneeded.)

4)The weights of ice cream cartons are normally distributed with a mean weight of 13 ounces and a standard deviation of 0.4 ounce.

(a) What is the probability that a randomly selected carton has a weight greater than 13.13 ounces?

(b) A sample of 36 cartons is randomly selected. What is the probability that their mean weight is greater than 13.13 ounces?