Question

**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

percentile of tire lifetimes.

(b) Find the

65th

percentile of 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 answers to two decimal places.

Answer #1

a)

mean μ= | 41 |

standard deviation σ= | 4.0 |

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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