Question

suppose that the weight of male babies less than 2 months old is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. a sample of 36 babies is selected. what is the probability that the average weight of the sample is less than 11.12 pounds? round to 4 decimal places.

Answer 1

Here, μ = 11.5, σ = 0.45 = 2.7/sqrt(36) and x = 11.12. We need to compute P(X <= 11.12). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (11.12 - 11.5)/0.45 = -0.84

Therefore,
P(X <= 11.12) = P(z <= (11.12 - 11.5)/0.45)
= P(z <= -0.84)
= 0.2005