Question

3. A Nielsen study indicates that 18 to 24 year olds spend a mean of 135 minutes watching video on their smartphones per month. Assume that the amount of time watching video on a smartphone per month is normally distributed and that the standard deviation is 15 minutes. a. What is the probability that an 18-to 24 year old spends less than 112 minutes watching video on his or her smartphone per month? b. What is the probability that an 18-to 24 year old spends between 112 and 158 minutes watching video on his or her smartphone per month? c. What is the probability that an 18 to 24 year old spends more than 158 minutes watching video on his or her smartphone per month? d. One percent of all 18 to 24 years old will spend less than how many minutes watching video on his or her smartphone per month?

Answer 1

Let X be the minutes of watching video on the smartphones by the 18 to 24 year old per month.

X ~ N( 135 , 15² )

a. The probability that an 18-to 24 year old spends less than 112 minutes watching video on his or her smartphone per month, P(X <112 )

b. The probability that an 18-to 24 year old spends between 112 and 158 minutes watching video on his or her smartphone per month , (112 < X < 158)

   

  

  

c. The probability that an 18 to 24 year old spends more than 158 minutes watching video on his or her smartphone per month , P(X > 158)

  

d. Let 'x' be the minutes that one percent of all 18 to 24 years old will spend less than minutes watching video on his or her smartphone per month.

P(X < x) = 0.01

Z value corresponding to probability 0.01 is 2.3263.

Χ– μ P(X < 112) = 112 - 135 15

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= (Z < 1.5333)

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(112 - 135 P(112< X < 158) = X - 158 - 135 15 15

= (-1.5333<Z < 1.5333)

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P(X> 158) = (* = 4, 158-135 15

= (Z > 1.5333)

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P(X<x) = (*-- - *- 135) = 0.01 15

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T - 135 - = 2.3263

x= 169.8945 ~ 170 minutes