The u. s. census bureau announced that the median sales price in 2014 for new homes was $282,800 and the mean sales price was $345,800. the standard deviation was $90,000.
a. if you selected a random sample of 100 homes sold, what is the probability that the sample mean would be less than $370,000?
b. if you selected a random sample of 100 homes sold, what is the probability that the sample mean would be between $350,000 and $360,000?

a) 0.9964

b) 0.3040

Step-by-step explanation:

Given data:

standard deviation =  $90,000

Mean sales price =$345,800

sample mean =  $370,000

Total number of sample = 100

calculate z score for [/tex](\bar x = 370000)[/tex]

z = 2.689

P(x<370000) = P(Z<2.689)

FROM STANDARD NORMAL DISTRIBUTION TABLE FOR Z P(Z<2.689) = 0.9964

B)

calculate z score for (\bar x = 350000)

z = 2.133

FROM NORMAL DISTRIBUTION TABLE Z VALUE FOR

SO,  = 0.9836 - 0.6796 = 0.3040

d

step-by-step explanation:

i used the pitagoras theoreme