Among smartphone owners 26-35 years of age, the average number of text messages

Question

Among smartphone owners 26-35 years of age, the average number of text messages sent per day follows an approximately Normal distribution with a mean of 42 and a standard deviation of 8.

(a) What percent of smartphone owners 26-35 years of age sent an average of more than 32 text messages per day?

(b) Fill in the blank: Approximately 30 percent of smartphone owners 26-35 years of age sent an average of less than text messages per day?

(c) Fill in the blank: Approximately 5 percent of smartphone owners 26-35 years of age sent an average of more than text messages per day.

Explanation / Answer

a) Percent of smartphone owners 26-35 years of age sent an average of more than 32 text messages per day

mean= 42 and std= 8

Since =42 and =8 we have:

P ( X>32 )=P ( X>3242 )=P ((X)/>(3242)/8)

Since Z=(x)/ and (3242)/8=1.25 we have:

P ( X>32 )=P ( Z>1.25 )

Use the standard normal table to conclude that:

P (Z>1.25)=0.8944= 89.44%

b) Approximately 30 percent of smartphone owners 26-35 years of age sent an average of less than is

Z value corresponding to 0.3 is -0.52

Z= X-mean/sigma

-0.52= X-42/8

-0.52*8= X-42

-4.16=X-42

X= 42-4.16= 37.84 = 38 (approximately)

Approximately 30 percent of smartphone owners 26-35 years of age sent an average of less than 38 tet messages per day.

c) Approximately 5 percent of smartphone owners 26-35 years of age sent an average of more than

Z score correspond to 0.05 is -1.64

Z=X-mean/sigma

-1.64= X-42/8

-1.64*8= X-42

-13.12= X-42

-13.12+42=X

28.88= X

X= 29 APRROXIMATELY.

Approximately 5 percent of smartphone owners 26-35 years of age sent an average of more than 29 text messages per day.

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