1.The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean of 2.63 inches and a standard deviation of 0.25 inches.

**a. What percentage of the apples in the orchard have diameters less than 1.95 inches? **

**b. What percentage of the apples in the orchard have diameters larger than 2.90 inches? **

**c. If a crate of 200 apples is selected from the orchard, approximately how many apples would you expect to have diameters greater than 2.90 inches? **

**d. What is the probability that a randomly selected apple in this orchard will have a diameter larger than 2.54 inches? **

**e. What is the probability that a randomly selected apple in this orchard will have a diameter between 1.95 inches and 2.9 inches? Interpret the meaning of this answer. **

2. A radar unit is used to measure the speed of automobile on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a standard deviation of 4 mph.

**a. Find the mean of all speeds if 3% of the automobiles travel faster than 72 mph. Round the mean to the nearest tenth.**

**b. Using the mean you found in part a, find the probability that a car is traveling between 70 mph and 75 mph. Interpret the meaning of this answer. **

**c. Using the mean you found in part a, find the 25th percentile for the variable “speed”.**