Rhee Leif is a pitcher for a local baseball team. It is known that the speed at

Question

Rhee Leif is a pitcher for a local baseball team. It is known that the speed at which he can throw a fastball is uniformly distributed between 82 and 94 miles per hour.

Round answers to four decimal places.

a) What type of variable is fastball speed? (Click to select)discretecontinuous

b) What is probability that the speed of a randomly selected fastball thrown by Rhee Leif is less than 86 miles per hour?

c) What is probability that the speed of a randomly selected fastball thrown by Rhee Leif is exactly 92 miles per hour?

d) What is the average speed of fastballs thrown by Rhee Leif?

e) What is the probability that the speed of a randomly selected fastball thrown by Rhee Leif is between 83 and 91 miles per hour?

f) What is the 25th percentile of the distribution of his fastball speeds?

g) What is the standard deviation of his fastball speeds?

h) A scout for an opposing team has been asked to find the specific speed that is exceeded by 10% of Rhee Leif's fastballs. What is that speed?

Explanation / Answer

here for uniform distirbution paramter a =82 and b=94

a)  type of variable is fastball speed -- continuous

b)  probability that the speed of a randomly selected fastball thrown by Rhee Leif is less than 86 miles per hour

=P(X<86)=(86-82)/(94-82)=0.3333

c) probability that the speed of a randomly selected fastball thrown by Rhee Leif is exactly 92 miles per hour =0

(as point probbaility for a continuous distribution is 0)

d)average speed of fastballs thrown by Rhee Leif =(a+b)/2 =(82+94)/2 =88

e) probability that the speed of a randomly selected fastball thrown by Rhee Leif is between 83 and 91 miles per hour =(91-83)/(94-82)=0.6667

f)

25th percentile of the distribution of his fastball speeds =a+0.25*(b-a)=82+0.25*(94-82)=85

g)standard deviation =(b-a)/(12)1/2 =3.464

h)

for 10th percentile value =a+0.1*(b-a) =82+0.1*(94-82)=83.2

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