Question

A survey of1000 new home buyers found that the prices paid were normally distributed with a mean of $185,000 and a standard deviation of $ 25,000. How many people paid between $160,000 and $210,000?

Answer 1

Solution:

Given that,

mean = = 185000

standard deviation = =   25000

P( 160000 < x < 21000 )

= P(( 160000 -185000 /25000 ) < (x - ) / < (210000- 185000 /25000 ) )

P(- 25000 / 250000 < z < 25000/25000)  

P(-1 < z < 1)

P(z < 1 ) - P(z < - 1)

using z table

0.8413 - 0.1587

= 0.6826

Probability = 0.6826

0.6826 * 1000 = 682.6

683 people paid between   160000 and 21000.