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.

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

Answer 1

The probability that a household views television between 5 and 11 hours a day is approximately 0.7653.

Step-by-step explanation:

To find the probability that a household views television between 5 and 11 hours a day, we can use the standard normal distribution.

First, we need to standardize the values of 5 hours and 11 hours using the formula: Z = (x - μ) / σ

For 5 hours: Z = (5 - 8.35) / 2.5 = -1.34

For 11 hours: Z = (11 - 8.35) / 2.5 = 1.06

Next, we can use a standard normal table or a calculator to find the corresponding probabilities. The probability of a household viewing between 5 and 11 hours a day is the difference between the two probabilities: P(5 < x < 11) = P(Z < 1.06) - P(Z < -1.34).

Using a standard normal table or calculator, we find that P(Z < 1.06) ≈ 0.8554 and P(Z < -1.34) ≈ 0.0901.

Therefore, the probability that a household views television between 5 and 11 hours a day is approximately 0.8554 - 0.0901 = 0.7653 (rounded to four decimal places).