Question

6. (7 pts.) The mean age of all used cars for sale in a newspaper one Saturday last month was7 years, with a standard deviation of 4 years. The distribution of ages is right-skewed. For a study to determine the reliability of classified ads, a reporter randomly selects 36 of these used (a) Mean of Distribution of T cars. SE of- (b) Find the probability that the mean age of the 49 cars selected is more than 8 years. P(E> 8)

Answer 1

Solution:

Given that,

mean = $\mu$ = 7 years

standard deviation = $\sigma$ = 4 years

n = 36

So,

a ) Mean distribution is  $\mu$$\bar x$

  $\mu$$\bar x$ = 7

Standard error of mean distribution is  $\sigma$_{$\bar x$}

$\sigma$_{$\bar x$} =  ($\sigma$ /$\sqrt$n)

$\sigma$_{$\bar x$}  = ( 4 / $\sqrt$36 )

$\sigma$_{$\bar x$}= 0.6667

b ) n = 49

So,

  $\mu$$\bar x$ = 7

$\sigma$_{$\bar x$} =  ($\sigma$ /$\sqrt$n) = ( 4 / $\sqrt$49 ) = 0.5714

p (  $\bar x$ > 8 )

= 1 - p (  $\bar x$ < 8 )

= 1 - p ( $\bar x$ - $\mu$$\bar x$/$\sigma$_{$\bar x$}) < ( 8 - 7 /0.5714 )

= 1 - p ( z < 1 /0.5714 )

= 1 - p ( z < 1.75 )

Using z table

= 1 - 0.9599

= 0.0401

Probability = 0.0401