Question

The amount of time spent by north american adults watching television per day is normally distributed with a mean of 7 hours and a standard deviation of 1.6 hours. (round your answers to four decimal places.)

what is the probability that a randomly selected north american adult watches television for more than 8 hours per day?

Answer 1

To calculate the probability that a randomly selected North American adult watches television for more than 8 hours per day, find the Z-score for 8 hours with a mean of 7 hours and a standard deviation of 1.6 hours, then subtract the corresponding left-tail probability from 1. The result is approximately 0.2660.

Step-by-step explanation:

To find the probability that a randomly selected North American adult watches television for more than 8 hours per day, given that the time spent watching television is normally distributed with a mean (μ) of 7 hours and a standard deviation (σ) of 1.6 hours, we use the Z-score formula:

Z = (X - μ) / σ

Where:
X = 8 hours
μ = 7 hours
σ = 1.6 hours

Calculating the Z-score:

Z = (8 - 7) / 1.6 = 0.625

Next, we look up the Z-score of 0.625 in the standard normal distribution table or use a statistical software to find the area to the left of Z. To find the area to the right (the probability of watching more than 8 hours), we subtract this value from 1.

Assuming the area to the left is approximately 0.734, the probability P(X > 8) is:

P(X > 8) = 1 - P(Z < 0.625) = 1 - 0.734 = 0.2660

This is the probability that a randomly selected North American adult watches television for more than 8 hours per day.