Reference no: EM132844726

A.μ=55.9 inches and 

 The heights of 10-year-old boys are Normally distributed with mean  =55.9

=5.7 inches.

1. Draw (or have a computer generate) a Normal curve with the parameters labeled. In your picture, shade in the region that represents the proportion of 10-year-old boys who are more than 61.6 inches. 
2. Find the area of the region you shaded, and interpret that area in two ways:

• as a proportion of all 10-year-old boys
• as a probability about one such boy

3- If we select one 10-year-old boy at random, what is the probability that he is more than 65 inches tall?

4- If we select one 10-year-old boy at random, what is the probability that he is more than 7 inches away from the mean? (He might be very tall, or he might be very short.)

5- What percentage of 10-year-old boys will be within 3 inches of the mean?

6- Find the 80th percentile of height - a value that separates the shortest 80% of 10-year-old boys from the tallest 20% of 10-year-old boys. Round your answer to the nearest tenth of an inch. 

B. Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately Normally distributed, with a standard deviation 0.015 mm. 

1. What proportion of ball bearings have a diameter more than 5.02 mm?
2. Any ball bearings that have a diameter less than 4.96 mm or greater than 5.04 mm are discarded. What proportion of ball bearings will be discarded?
3. Using the results of the last problem, if 20,000 ball bearings are manufactured in a day, how many should the plant manager expect to discard?
4. If an order comes in for 40,000 ball bearings, how many bearings should the plant manager manufacture if the order states that all the ball bearings must be between 4.975 mm and 5.025 mm? (You mustexplain how you are getting your answer)