Question

.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 1

P(Y > 121) = 1 - P(Y < 121) = 1 - P(z < (121 - 115)/6) = 1 - P(z < 1) = 1 - 0.84134 = 0.15866

P(Y ≤ c) = 0.15
P(Y ≤ c) = 1 - 0.85
P(Y ≤ c) = 1 - P(z ≤ 1.0365)
P(Y ≤ c) = P(z ≤ -1.0365)
Thus, (c - 115) / 6 = -1.0365
c - 115 = -6.219
c = -6.219 + 115
c = 108.781