We discovered that 1,001 GSS 2014 respondents watched television for an average

Question

We discovered that 1,001 GSS 2014 respondents watched television for an average of 2.94 hours per day, with a standard deviation of 2.60 hours. Answer the following questions assuming the distribution of the number of television hours is normal.

What is the Z score for a person who watches more than 8 hours per day?

What proportion of people watch television less than 5 hours per day? How many does this correspond to in the sample?

What number of television hours per day corresponds to a Z score of +1?

What is the percentage of people who watch between 1 and 6 hours of television per day?

Explanation / Answer

as we know that z score =(X-mean)/std deviaiton

hence

a)  Z score for a person who watches more than 8 hours per day =(8-2.94)/2.6 =1.9462

b)proportion of people watch television less than 5 hours per day =P(X<5)=P(Z<(5-2.94)/2.6)=P(Z<0.7923)=0.7859

number correspond to in the sample =np =1001*0.7859=~787

c) number of television hours per day corresponds to a Z score of +1 =mean+z*std deviation =2.94+1*2.6=5.54

d) percentage of people who watch between 1 and 6 hours of television per day =P(1<X<6)

=P((1-2.94)/2.6<Z<(6-2.94)/2.6)=P(-0.7462<Z<1.1769)=65.26%

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