Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of   180   feet and a standard deviation of   60feet. Let   X=   distance in feet for a fly ball.

In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest   0.01 .

  X∼    (pick one) EUBN   (    ,    ) .

For a random fly ball, what is the probability that this ball traveled fewer than   220   feet?   P(X<220)=    .

The   80th   percentile of the distribution of fly balls is given by   P(X<  )=0.80 .

Answer 1

As the distribution is normal we can convert X into z

Now we want to find P(X<220)=

So Answer is 0.7475

Now we want The   80th   percentile of the distribution of fly balls is given by   P(X< x)=0.80

So using z table we got P(z<0.842)=0.80

Now

So x=(0.842*60)+180=230.52

So answer is

The   80th   percentile of the distribution of fly balls is given by   P(X<230.52 )=0.80 .