Suppose the maximum number of pounds an athlete at the high

Suppose the maximum number of pounds an athlete at the high school level is able to bench press has roughly a bell-shaped distribution with mean 90.0 and standard deviation 12.0. Use the Empirical Rule to answer the following questions.

a) What is the percentage of athletes who are able to bench press more than 78.0 pounds?

b) What is the percentage of athletes who are able to bench press between 66.0 pounds and 102.0 pounds?

c) What is the percentage of athletes who are able to bench press more than 114.0 pounds?

Solution

X -- the no of athlets follow a Normal with (90,12)

a) First convert x into z score so that we use z table.

x>78 is equal to z>-1

P(Z>-1) = 0.8413

84.13% are able to bench press >78 pounds

b) P(66

81.85% of athlets are able to bench press between 66.0 pounds and 102.0 pounds

c) P(X>114) = P(Z>2) = 0.0228

2.28 % are able to bench more than 114 pounds