Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 255 feet and a standard deviation of 37 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 278 feet.____ Round to 4 decimal places.

c. Find the 70th percentile for the distribution of distance of fly balls. Round to 2 decimal places. ___ feet

Fill in "___" please.

Answer 1

a) X follows normal Distribution.

It is represented as X~(mean, SD)

"X~N(225,37)"

b)

We have to find probability that a randomly hit ball travels less than 278 feet.

x for this case is 278. we have mean and distribution with us.

Now we need to calculate z-value. (why?)

The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is 5 and the standard deviation is 2, the value 11 is 3 standard deviations above (or to the right of) the mean. The calculation is: x = mean + (z) SD that is  5 + (3) (2) = 11 (6.1) The z-score is 3.

Please refer Pictures attached

z scores and how to read them:

z score could be positive or negative.

when z score is positive like in our case:

when Z score is Negative:

c) "244.61"

Please find attached pic.