Question

The average length of a viewing session on twitch is 40 minutes, with a variance of 100. in a random sample of 50 twitch viewing sessions, what is the probability that the sample mean is less than 42?

Answer 1

The probability that the sample mean is less than 42 is 0.55567

Given,

Population mean, μ = 40

Standard deviation, σ = 100

Sample size, n = 50

Sample mean, ₓ⁻ = 42

We have to find the standard score, z =(ₓ⁻ – μ) / (σ/√n)

Substituting the values we get,

Z < (ₓ⁻ – μ) / (σ/√n)

Z < (42 – 40) / (100 / √50)

Z < (2) / (100/ 7.07)

Z < (2 / 14.44)

Z < 0.14

Using the z score table we get the corresponding z score as 0.5567

That is,

The probability that the sample mean is less than 42 is 0.55567

Learn more about probability here: https://brainly.com/question/14801624

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