. A youth sports team is trying to determine how many small, medium, and large s

Question

. A youth sports team is trying to determine how many small, medium, and large size jerseys to buy for its players. Small jerseys fit children up to 60 pounds. Medium jerseys fit children 60-75 pounds. Large jerseys fit children 75-110 pounds. The distribution of the players’ weights is normally distributed with a mean of 70 pounds and a standard deviation of 10 pounds. If there are 50 kids on the team, how many of each jersey should the team purchase? Be sure to include all relevant Minitab Express output and clearly identify your answers by writing a sentence. (20 points)

Explanation / Answer

small <= 60

medium 60-75

large 75-110

mean = 70

standard dev = 10

a)small =

For x = 60, the z-value z = (60 - 70) / 10 = -1

Hence P(x < 60) = P(z < -1) = [area to the left of -1] = 0.1587

b) medium

For x = 60 , z = (60 - 70) /10 = 0 and for x = 75, z = (75 - 70) / 10 = 0.5

Hence P(60 < x < 75) = P(-1 < z < 0.5) = [area to the left of z = 0.5] - [area to the left of -1]

= 0.6915 - 0.1587 = 0.5328

c) large

For x = 75 , z = (75 - 70) /10 = 0.5 and for x = 110, z = (110 - 70) / 10 = 4

Hence P(75 < x < 110) = P(0.5 < z < 4) = [area to the left of z = 4] - [area to the left of 0.5]

= 0.9998 - 0.6915 = 0.3083

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