Question

Scores on a standard test of mechanical aptitude are normally distributed with a mean of 72 and a s. d. of 12. If 36 subjects are randomly selected, the probability that their mean score will be at least 69 is (round to the 3rd decimal place).

Answer 1

Solution :

Given that ,

mean = $\mu$ = 72

standard deviation = $\sigma$ = 12

n = 36

$\mu$$\bar x$ = 72

$\sigma$$\bar x$ = $\sigma$ / $\sqrt$ n = 12/ $\sqrt$36 = 2

P($\bar x$ > 69) = 1 - P($\bar x$ <69 )

= 1 - P[( $\bar x$ - $\mu$ $\bar x$ ) / $\sigma$ $\bar x$ < (69-72) /2 ]

= 1 - P(z <-1.5 )

Using z table

= 1 - 0.0668

= 0.9332

probability= 0.933