Suppose that the distance of fly balls hit to the outfield (in baseball) is norm

Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 200 feet and a standard deviation of 50 feet. Let X = distance in feet for a fly ball.

Give the distribution of X.
X ~ ( , )

If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 180 feet? (Round your answer to four decimal places.)

Find the 80th percentile of the distribution of fly balls. (Round your answer to one decimal place.)

Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.)

P(X < k) =

Explanation / Answer

Mean = 200 feet

Standard deviation = 50feet

X ~ (200,50)

P(X < A) = P(Z < (A - mean)/standard deviation)

P(the ball traveled fewer than 180 feet) = P(X < 180)

= P(Z < (180 - 200)/50)

= P(Z < -0.4)

= 0.3446

P(X < k) = P(Z < (k - 200)/50) = 0.8

From the standard normal distribution table, (k - 200)/50 = -0.84

k = 158 feet

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