Question

You may need to use the appropriate appendix table to answer this question. Television viewing reached a new high when the Nielsen Company reported a mean daily viewing time of 8.35 hours per household.† Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.

(a) What is the probability that a household views television between 5 and 11 hours a day? (Round your answer to four decimal places.)

(b) How many hours of television viewing must a household have in order to be in the top 2% of all television viewing households? (Round your answer to two decimal places.) hrs

(c) What is the probability that a household views television more than 4 hours a day? (Round your answer to four decimal places.)

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	8.35
std deviation   =σ=	2.500

  probability that a household views television between 5 and 11 hours a day:

probability =

P(5<X<11)

=

P(-1.34<Z<1.06)=

0.8554-0.0901=

0.7653

b)

for top 2% crtiical value z=2.05

hence corresponding time =mean+z*std deviaiton=13.48

c)

probability that a household views television more than 4 hours a day:

probability =

P(X>4)

=

P(Z>-1.74)=

1-P(Z<-1.74)=

1-0.0409=

0.9591