Question

# Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is...

Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean

=μ41

and a standard deviation

=σ4

.

(a) Find the

13th

(b) Find the

65th

(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 answers to two decimal places.

a)

 mean μ= 41 standard deviation σ= 4
 for 13th percentile critical value of z= -1.13 therefore corresponding value=mean+z*std deviation= 36.48

( try 36.50 if above comes wrong due to rounding error )

b)

 for 65th percentile critical value of z= 0.39 therefore corresponding value=mean+z*std deviation= 42.56

( try 42.54 if above comes wrong)

c)

 for 25th percentile critical value of z= -0.67 therefore corresponding value=mean+z*std deviation= 38.32

( try 38.30 if above comes wrong)

d)

 for 4th percentile critical value of z= -1.75 therefore corresponding value=mean+z*std deviation= 34.00

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