Question

A worldwide organization of academics claims that the mean IQ score of its members is 112, with a standard deviation of 15. A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 114.4. If the organization's claim is correct, what is the probability of having a sample mean of 114.4 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. xs ?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 112

standard deviation = $\sigma$ = 15

n = 35

$\mu$_{$\bar x$} = 112

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 15/ $\sqrt$ 35=2.535

P($\bar x$ <114.4 ) = P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (114.4-112) / 2.535]

= P(z < 0.95)

Using z table

probability=  0.8289