We discovered that 650 GSS respondents in 2006 watched television for an average

Question

We discovered that 650 GSS respondents in 2006 watched television for an average of 2.98 hrs/day, with a standard deviation of 2.4 hours. Answer the following questions, assuming the distribution of the number of television hours is normal.

A) What is the Z score for a person who watches more than 8 hrs/day.

B) What proportion of people watch 5 hrs/day or more television?

C) How many does this correspond to in the sample?  

D) What number of television hours per day corresponds to a Z +1.

E) What is the percentage of people who watch between 1 and 6 hours of television per day? Please round to a whole number

Explanation / Answer

= 2.98

= 2.4

a) P(X>8)

Z-Score = (8-2.98)/2.4 = 2.09

P(Z>2.09) = 1-P(Z<2.09) = 1-0.9817= 0.0183

b)P(X>5)

Z-Score = (5-2.98)/2.4 = 0.84

P(Z>0.84) = 1-P(Z<0.84) = 1-0.7995= 0.2005

c) 650*0.2=130

It corresponds to around 130 people i.e. 20%

e)

P(1<X<6)

Z- Score for 1, Z1= (1-2.98)/2.4 = -0.825

Z- Score for 6, Z2= (6-2.98)/2.4 = 1.25

We have,

P(Z<1.25) = 0.8944

P(-0.825<Z) = 1-0.2061= 0.7939

Area between these two = 0.8944-0.7939=0.1005

d) Z=(X-)/

Z=X-

X=Z+

It is possible when both mean and SD are 1 for any X score to have a Z+1

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