Question

The Average sales price of single-family houses in Charlotte is $210,000 with a standard deviation of $35,000. A random sample of 49 single-family houses in Charlotte is selected. Let x bar represent the mean sales price of the sample.

1. Find the mean and standard deviation of x bar ,i.e, u x bar and o x bar .

2. What is the probability that the sample mean sales price x bar is more than $220,000?

Answer 1

Solution :

Given that ,

mean = = 210000

standard deviation = = 35000

n = 49

(a)

= 210000

= / n = 35000 / 49 = 5000

(b)

P( > 220000) = 1 - P( < 220000)

= 1 - P[( - ) / < (220000 - 210000) / 5000]

= 1 - P(z < 2)

= 1 - 0.9772

= 0.0228