Question

Assume the selling prices of homes in a particular community follow a normal distribution with a mean of ​$289, 000 and a standard deviation of ​$43,300. Complete parts a through c.

a. Determine the range of selling prices in this community that includes one standard deviation around the mean.

The range is from $________ to ​$_________.

​(Type integers or decimals. Use ascending​ order.)

b. Determine the range of selling prices in this community that includes two standard deviation around the mean.

The range is from $________ to ​$_________.

​(Type integers or decimals. Use ascending​ order.)

c.. Determine the range of selling prices in this community that includes three standard deviation around the mean

The range is from $________ to ​$_________.

​(Type integers or decimals. Use ascending​ order.)

Answer 1

Given that,

= $289000

= $43300

Using Empirical rule,

(a)P(289000 - 1(43300)< X < 289000 + 1(43300)) = 68%

P(289000 -43300 < X < 289000+43300) = 68%

P(245700 < X <332300) = 68%

Answer =The range is from $245700 , $33230

(b)

P(289000 - 2(43300)< X < 289000 + 2(43300)) = 95%

P(289000 -86600 < X < 289000+86600) = 95%

P(202400 < X <375600) = 95%

Answer =The range is from $202400 , $375600

(c)

P(289000 - 3(43300)< X < 289000 + 3(43300)) = 99.7%

P(289000 -129900 < X < 289000+129900) = 99.7%

P(159100< X <418900) = 99.7%

Answer =The range is from $159100 , $418900