Question

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,060. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $495. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.)

What percent of the adults spend more than $2,575 per year on reading and entertainment?

What percent spend between $2,575 and $3,300 per year on reading and entertainment?

What percent spend less than $1,225 per year on reading and entertainment?

Answer 1

A) P(x> 2575) = 14.92%

B) P(2575 < X<3300) = 14.32%

C) ( P X < 1225) = 4.55%

Explanation:

Given data:

`\mu = $2060`

`\sigma  = $495`

a) P(x> 2575)

1 - P(X<2575)

`1 - P((x-\mu)/(\sigma) < (2575 - 2060)/(495))`

`1 - P(z < (515)/(495))`

1 - P( Z< 1.04)

1 - 0.8508

0.1492

14.92%

B) P(2575 < X<3300)

`P((2575 - 2060)/(495) <x < (3300 -2060)/(495))`

P (1.04 < z< 2.51)

P(z <2.51) - P(Z<1.04)

0.994 - 0.8508 = 0.1432 = 14.32%

C) ( P X < 1225)

`P( (x - \mu)/(\sigma) < (1225 - 2060)/(495))`

`P( z < (-835)/(495)`

P ( Z< -1.69)

= 0.0455 = 4.55%