Social networking sites have grown in popularity as users cr

Social networking sites have grown in popularity as users create web pages loaded with music, photographs, and profiles. Hitwise reported that the mean time spent by a use a Facebook during April 2008 was 20 minutes, 52 seconds. Suppose the distribution of time spent at Facebook per month is normal, the standard deviation is 4.5 munutes, and a Facebook user is selected at random.

a) Find the probability that the user spends less than 16 minutes per month at the site.

b) Find the probability that the user spends between 20 and 30 minutes per month at the site.

c) Find a value t such that only 2.5% of all Facebook users spend more than t minutes at Facebook per month.

Solution

mean= 20 minutes, 52 seconds = 20.867 minutes

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a) Find the probability that the user spends less than 16 minutes per month at the site.

P(X<16) = P((X-mean)/s <(16-20.867)/4.5)

=P(Z<-1.08) =0.1401 (from standard normal table)

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b) Find the probability that the user spends between 20 and 30 minutes per month at the site.

P(20<X<30) = P((20-20.867)/4.5<Z<(30-20.867)/4.5)

=P(-0.19<Z<2.03)

=0.5542 (from standard normal table)

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c) Find a value t such that only 2.5% of all Facebook users spend more than t minutes at Facebook per month.

P(X>c)=0.025

--> P(Z<(c-20.867)/4.5) =1-0.025 =0.975

--> (c-20.867)/4.5 = 1.96 (from standard normal table)

So c=20.867+1.96*4.5=29.687