Find the probability.

Question

It is reported that children between 2 and 6 years old watch an average of 20 hours of TV per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages 2 and 6 are randomly selected, find the probability that the mean of the number of hours they watch TV will be greater than 21.3 hours.

Answer 1

Let x = time watching TV

n = 20

σ = 3

S.E. = σ / √n, so 3 / √20, and that makes the S.E. = 0.671

Now to find the probability of (x̄ > 21.3)

= 21.3 - 20 / 0.671

= x > 1.9374

--Look up Z score --

=0.0263 * 100

=2.63%

The probability that the mean number of hours watching TV is greater than 21.3 hours is 2.63%.