Question

3. Normal Distribution for the sample means. The average teacher's salary in New Jersey (ranked first among states ) is $52174. Suppose that the distribution is normal with a standard deviation equation to $7500. If we sample 100 teachers' salaries , what is the probability that the sample mean is less than $50000?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 52174

standard deviation = $\sigma$ = 7500

n = 100

$\mu$_{$\bar x$} =   $\mu$ = 52174

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 7500 / $\sqrt$ 100 = 750

P($\bar x$ < 50000) = P(($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (50000 - 52174) / 750 )

= P(z < -2.90)

Using z table

= 0.0019