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.Ace! Professional tennis player Rafael Nadal hits the ball extremely hard. His first-serve speeds follow a Normal distribution with mean 115 miles per hour (mph) and standard deviation 6 mph. Choose one of Nadal’s first serves at random. Let Y = its speed, measured in miles per hour. Find P(Y > 121) and interpret the result.  What is P(Y ≥ 121)? Explain. Find the value of c such that P(Y ≤ c) = 0.15. Show your work

Answer :

MissPhiladelphia
We are given with
mean = 115
std dev = 6

First problem
P (Y > 121)
The z score for this is
z = (115 - 121) / 6
z = -1 which corresponds to a value of 0.1587
P (Y > 121) = 1 - 0.1587
= .8413 or 84.13%

Next problem
P(Y ≤ c) = 0.15
corresponds to z score of
z = -1.04
calculating for c
-1.04 = (115 - c) / 6
c =  121.24

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