Question

A newspaper article reported that people spend a mean of 7 hours per day watching TV, with a standard deviation of 1.9 hours. A psychologist would like to conduct interviews with the 20% of the population who spend the most time watching TV. She assumes that the daily time people spend watching TV is normally distributed. At least how many hours of daily TV watching are necessary for a person to be eligible for the interview? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Answer 1

To be eligible for the interview, a person needs to watch at least 8.6 hours of TV daily.

Step-by-step explanation:

To determine the number of hours necessary for a person to be eligible for the interview, we need to find the value of X, which represents the number of hours for a person to be in the top 20% of TV watchers. Since the distribution is normal, we can use the Z-score formula to find the standard score corresponding to the 20th percentile. The formula for the Z-score is (X - mean) / standard deviation. Rearranging the formula to solve for X, we have X = (Z * standard deviation) + mean. Plugging in the values, we get X = (0.8416 * 1.9) + 7 = 8.59904 hours. Therefore, a person will need to watch at least 8.6 hours of TV daily to be eligible for the interview.