Question

The amount of time x in hours spent each week watching television by children under twelve is normally distributed with mean 24.5 hours and standard deviation 6.23 hours. The percentage that a randomly selected child spends at least 30 hours each week watching television is about:

Answer 1

18.867%

Explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 30 hours

μ is the population mean = 24.5 hours

σ is the population standard deviation = 6.23 hours

z = 30 - 24.5 /6.23

z = 0.88283

Probability value from Z-Table:

P(x<30) = 0.81133

The percentage that a randomly selected child spends at least 30 hours each week watching television is calculated as:

At least 30 hours = 30 hours or more = ≥ 30

Hence,

P(x>30) = 1 - P(x<30)

= 1 - 0.81133

= 0.18867

Converting to percentage

0.18867 × 100

= 18.867%

The percentage that a randomly selected child spends at least 30 hours each week watching television is 18.867%