Question

Penn State Fleet which operates and manages car rentals for Penn State employees found that the tire lifetime for their vehicles has a mean of 50,000 miles and standard deviation of 3500 miles.

What is the probability that the sample mean lifetime for these 50 vehicles exceeds 51,000?

Answer 1

Solution :

Given that,

mean = $\mu$ = 50000

standard deviation = $\sigma$ =3500

n=50

$\mu$$\bar x$ = $\mu$ =50000

$\sigma$$\bar x$ = $\sigma$ / $\sqrt$ n = 3500/ $\sqrt$50 = 494.9748

P($\bar x$ >51000 ) = 1 - P($\bar x$ < 51000)

= 1 - P[($\bar x$ - $\mu$ $\bar x$ ) / $\sigma$ $\bar x$ < (51000-50000) /494.9748 ]

= 1 - P(z < 2.02)

Using z table

= 1 - 0.9783

=0.0217

probability= 0.0217