In the NFL there is a strict policy about the amount of pres

In the NFL there is a strict policy about the amount of pressure in each game ball. To ensure all game balls used will be able to withstand all environmental and game conditions Wilson randomly tests selected footballs before shipping. They have found that the PSI within each football has a normal distribution with mean of 13 and standard deviation of 0.75

1. what is the probability that a game ball will have less than 10.92 PSI after a normal game?

2. what is the probability that a game ball will have more than 13.5 PSI after a normal game?

3. after a normal game what range should 95% of the game balls PSI be?

Solution

1. what is the probability that a game ball will have less than 10.92 PSI after a normal game?

P(X<10.92) = P((X-mean)/s <(10.92-13)/0.75)

=P(Z<-2.77) = 0.0028 (from standard normal table)

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2. what is the probability that a game ball will have more than 13.5 PSI after a normal game?

P(X>13.5) = P(Z>(13.5-13)/0.75)

=P(Z>0.67) =0.2514 (from standard normal table)

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3. after a normal game what range should 95% of the game balls PSI be?

P(X<x)=0.95

--> P(Z<(x-13)/0.75) =0.95

--> (x-13)/0.75 = 1.64 (from standard normal table)

So x= 13+1.64*0.75 =14.2