Question

3. The amount of time it takes to complete a task is normally distributed with a mean of 34 minutes and a standard deviation of 4 minutes. If I take a sample of 24 people how many of those 24 people on average will take over 37 minutes to do the task?

Answer 1

Here, μ = 34, σ = 4 and x = 37. We need to compute P(X >= 37). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (37 - 34)/4 = 0.75

Therefore,
P(X >= 37) = P(z <= (37 - 34)/4)
= P(z >= 0.75)
= 1 - 0.7734 = 0.2266

If 24 people had taken the task, 0.2266*24 = 5.44
i.e. 5 are expected to take over 37 minutes