Please help me.

Question

The mean weight of 5-year-old children is 39.5 pounds and standard deviation is 3.2 pounds if a sample of 52 5-year-old children is selected find the probability that the mean of the sample will be greater than 37.5 pounds assume the data are normally distributed based on your answer would you consider the group overweight

Answer 1

In general:

P(M < a) = P( (a - mu)/(SD/sqrt(n)), where M is sample mean, mu is population mean, SD is population standard deviation and n is sample size

Here a is 37.5, mu is 398.5, SD = 3.2 and n = 52

P(M > 37.5)

= P( z > (37.5 - 39.5)/(3.2/sqrt(52))

= P(z > -4.5) = 1 - P(z < -4.5) ~ 1