Question

# You may need to use the appropriate appendix table to answer this question. Television viewing reached...

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 3 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 4% of all television viewing households? (Round your answer to two decimal places.)

Solution :

Given that ,

mean = = 8.35

standard deviation = = 2.5

a)

P(3 < x <11 ) = P((3-8.35)/ 2.5) < (x - ) /  < (11-8.35) / 2.5) )

= P( -2.14 < z < 1.06)

= P(z < 1.06 ) - P(z < -2.14)

= 0.8554 - 0.0162

= 0.8392

Probability = 0.8392

b)

The z distribution of 4% is

P(Z > z ) = 4%

1 - P(Z < z ) = 0.04

P(Z < z ) = 1-0.04

P(Z < z ) = 0.96

P(Z < 1.75 ) = 0.96

z = 1.75

Using z-score formula

X = z* +

X = 1.75 * 2.5 + 8.35

X = 12.73

12.73 hours of television viewing must a household have in order to be in the top 4% of all television viewing households

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