Question

It has been recently reported that the mean daily TV viewing time per US household is 8.35 hours (µ=8.35). Assume that daily TV viewing time per US household is normally distributed with a standard deviation of 2.5 hours (σ=2.5).

Question:

Suppose that Mr.Edward's household is in the top 5% of all households in terms of time spent watching TV. Then,
Mr. Edward's household spends at least ----- hours (per day) watching TV. Round to 1 decimal point. Do not add the word "hours" in your answer.

Answer 1

Given,

= 8.35 , = 2.5

We convert this to standard normal as

P(X < x) = P( Z < x - / )

We have to calculate x such that P( X > x) = 0.05

That is

P( Z > x - / ) = 0.05

P(Z < x - / ) = 0.95

From the Z table, critical value at 0.95 level is 1.645

Therefore,

x - / = 1.645

Put the values of and in above expression and solve for x

x - 8.35 / 2.5 = 1.645

x = 12.4625

x = 12.5 (Rounded to 1 decimal places)

Mr. Edward's household spends at least 12.5 hours (per day) watching TV.