Question

Find C. with work shown please

A report announced that the median sales price of new houses sold one year was $211,000, and the mean sales price was $271,900. Assume that the standard deviation of the prices is $100,000. Complete parts (a) through (d) below. CD. The sampling distribution will be approximately normal. (c) If you select a random sample of n = 100, what is the probability that the sample mean will be less than $300,000? The probability that the sample mean will be less than $300,000 is (Round to four decimal places as needed.)

Answer 1

Solution :

Given that ,

$\mu$_{$\bar x$} = 271,900

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 100,000 / $\sqrt$ 100 = 10000

P($\bar x$ < 300,000) = P(($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (300,000 - 271,900) / 10000)

= P(z < 2.81)

Using z table

= 0.9975