Question

A Nielsen study indicates that 18- to 34-year olds spend a mean of 93 minutes watching video on their smartphones per week. Source: Data extracted from bit.ly/2rj8GHm. Assume that the amount of time watching video on a smartphone per week is normally distributed and that the standard deviation is 15 minutes. a. What is the probability that an 18- to 34-year-old spends less than 77 minutes watching video on his or her smartphone per week? b. What is the probability that an 18- to 34-year-old spends between 77 minutes and 109 minutes watching video on his or her smartphone per week? c. What is the probability that an 18- to 34-year-old spends more than 109 minutes watching video on his or her smartphone per week? d. One percent of all 18- to 34-year-olds will spend less than how many minutes watching video on his or her smartphone per week?

Answer 1

mu=93

sd=15

Distribution is normal

(i) Z= (Xbar-mu)/sd

P(Xbar<77)

Z= (77-93)/15 =-1.066667

Hence P(Z<-1.066667) = 0.1430611 (From Z table check the area under the curve from -inf till -1.066)

So Here we can say that 0.1430611 is the probability that an 18- to 34-year-old spends less than 77 minutes watching video on his or her smartphone per week

(ii) P(77<Xbar<109)

Z= (Xbar-mu)/sd

=(109-93)/15

=1.066667

P(-1.06667<Xbar<1.06667)

= 0.7138778 (From Z table check the area under the curve from -1.066 till -1.066)

(iii)P(Xbar>109)

P(Z>+1.066667)

=0.1430611 (From Z table check the area under the curve from 1.066667 till inf)

(iv) z value for 1% is -2.326348 from z table

Z= (Xbar-mu)/sd

-2.326348=(Xbar-93)/15

Xbar= 58.10478

Hence 1% of the 18-34 years old will watch videos less than 58 mins/week

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