Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 266 feet and a standard deviation of 44 feet. Let X be the distance in feet for a fly ball.
a. What is the distribution of X? X ~ N

b. Find the probability that a randomly hit fly ball travels less than 240 feet. Round to 4 decimal places

c. Find the 75th percentile for the distribution of distance of fly balls. Round to 2 decimal places

Answer 1

a). X follows normal distribution.

where, = 266 and = 44

b).the probability that a randomly hit fly ball travels less than 240 feet be:-

= 0.2773

[ in any blank cell of excel type =NORMDIST(240,266,44,TRUE) press enter ]

c).let, x be the 75th percentile for the distribution of distance of fly balls.

according to the problem,

[ in any blank cell of excel type =NORMINV(0.75,266,44)   press enter ]

the 75th percentile for the distribution of distance of fly balls = 295.68 feet.

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