Question

The sale prices of homes in a particular region are found to be normally distributed with a mean of 250,000, and a standard deviation of 20,000.

If 1,000 people bought homes in this region, how many people paid between 230,000 and 270,000?

I'm not given any tables or graphs. How do I solve this?

Answer 1

Solution :

Given that ,

mean = = 250000

standard deviation = = 20000

P(230000 < x < 270000) = P((230000 - 250000/ 20000) < (x - ) / < (270000 - 250000) / 20000) )

P(230000 < x < 270000) = P(-1 < z < 1)

P(230000 < x < 270000) = P(z < 1) -P(z < -1) Using standard normal table,

P(230000 < x < 270000) = 0.8413 - 0.1587 = 0.6826

So , 1000 * 0.6826 = 682.6

682.6 people paid between 230,000 and 270,000 .