Television iewing reached a new high when the global information and measurement

Question

Television iewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. Use a normal probablity distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per a. What is the probability that a household views television between 4 and 10 hours a day (to 4 decimals) b. How many hours of teles on viewing must a household havin order to be the top 8% of all tee son vewing households (to 2 de mais)? hours C. What is the probability that a household views television more than 5 hours a day (to 4 deomas)? Check My Work (a remainin

Explanation / Answer

Mean is 8.35 and s is 2.5, z is given as (x-mean)/s

a) P(4<x<10)=P((4-8.35)/2.5<z<(10-8.35)/2.5)=P(-1.74<z<0.66)=P(z<0.66)-(1-P(z<1.74)). from normal distribution table we get 0.7454-(1-0.9591)=0.7045

b) for top 8% we need a value at bottom 92% which from normal distribution gives a z of 1.41, thus the value is mean+z*s =8.35+2.5*1.41=11.875

c) P(x>5)=P(z>(5-8.35)/2.5)=P(z>-1.34) or P(z<1.34), from normal distribution table we get 0.9099

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