6. value: 1.70 points According to a government study among adults in the 25- to

Question

6. value: 1.70 points 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 $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456. (Round z-score computation to 2 decimal places and your final answers to 2 decimal places.) a. What percent of the adults spend more than $2,600 per year on reading and entertainment? Percent b. What percent spend between $2,600 and $2,900 per year on reading and entertainment? Percent c. What percent spend less than $1,200 per year on reading and entertainment? Percent

Explanation / Answer

SolutionA:

mean=2020

sd=456

solutionA:

P(X>2600)

z=X-mean/sd

=2600-2020/456

=1.27

P(Z>1.27)

=1-P(Z<1.27)

=1-0.898

=0.102

=10.2%

ANSWER:10.2%

Solutionb:

P(2600<X<2900)

P(2600-2020/456<Z<2900-2020/456)

P(1.27<Z<1.93)

=P(Z<1.93)-P(Z<1.27)

=0.0752

=7.52%

ANSWER:7.52%

Solutionc:

P(X<1200)

z=1200-2020/456

P(Z<-1.8)

=1-P(Z<1.8)

=1-0.9641

=0.0359

=3.59%

ANSWER:3.59%

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