Question

Suppose 100 randomly selected members of a Karaoke club associated with a website are asked how much time they spend on the website during the week. Assume that the population mean isμ = 4 standard deviation is known to be σ = 2.5.
A.) What is the probability that the sample mean x̄ is exactly 4.2?

B.) What is the probability that the sample mean x̄ is greater than 4.2?

C.) What is the probability that the sample mean x̄ differs from the true population mean by more than 0.2?

Answer 1

For mean amount of time,

Sample mean = 4

Standard error =

Hence,

a) P(x̄ = 4.2) = 0

b) P(x̄ > 4.2) = P(z > (4.2 - 4)/0.25) = P(z > 0.8) = 0.2119

c) P(Sample mean differs by more than 0.2)

= 1 - P(Sample mean within 0.2)

$= 1 - P(-\frac{0.2}{0.25} < z < \frac{0.2}{0.25})$

= 1 - P(-0.8 < z < 0.8)

= 1 - 0.5763

= 0.4237