Question

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean = 41 and standard deviation = 4. Use the TI-84 Plus calculator to answer the following.

(a) Find the 21st percentile of the tire lifetimes.

(b) Find the 73rd percentile of the tire lifetimes.

(c) Find the first quartile of the tire lifetimes.

(d) The tire company wants to guarantee that its tires will last at least a certain number of miles. What number of miles (in thousands) should the company guarantee so that only 4% of the tires violate the guarantee?

Round the answers to at least two decimal places.

Answer 1

a)

for 12.1th percentile critical value of z=	-1.170
therefore corresponding value=mean+z*std deviation=	36.3200

b(

for 73th percentile critical value of z=	0.613
therefore corresponding value=mean+z*std deviation=	43.4513

C)

for 25th percentile critical value of z=	-0.674
therefore corresponding value=mean+z*std deviation=	38.3020

D)

for 4th percentile critical value of z=	-1.751
therefore corresponding value=mean+z*std deviation=	34.00 Thousand miles