Question

A sample of n=67 sold homes from a population of 11,500 sold homes in the past year, found an average sale price to be $153,500 with a σ_n-1 = $55,175.

What is the value for the standard deviation of this sample?

What percentage of homes sold within + $10,000 of the average sale price?

What percentage chance will the average sale price of homes be > $140,000?

What percentage chance will the average sales price be < $150,000?

Answer 1

Mean, = $153,500

Standard deviation, = $55,175

n = 67

Value for the standard deviation of this sample = 55,175/√67

= $6740.7

Percentage of home sold within $10,000 of the average sale price = P(|Z| ≤ 10000/6740.7) = P(|Z| ≤ 1.4834)

= 0.8621 = 86.21%

Percentage of home having average sales price of homes above $140,000 is P{Z > (140,000 - 153,500)/6740.7}

= P(Z > -2) = 0.9772 = 97.72%

Percentage of home having average sales price below $150,000

= P{Z (150,000 - 153,500)/6740.7}

= P(Z < -0.519) = 0.3018 = 30.18%