Heights of children entering kindergarten are normally distributed with a mean of 103 cm and a standard deviation of 1.27 cm.What is the probability that a random sample of 8 children will have an average height more than 103.5 cm?
A) 0.8665
B) 0.6517
C) 0.3483
D) 0.1335

Question

Quizplus · Accepted Answer

To find the probability that a random sample of 8 children will have an average height more than 103.5 cm, we use the formula for the standard error of the mean: SE = σ / √n, where σ is the standard deviation and n is the sample size. Here, σ = 1.27 cm and n = 8, so SE = 1.27 / √8 = 0.449. We then find the Z-score for 103.5 cm: Z = (X - μ) / SE = (103.5 - 103) / 0.449 = 1.114. Using the Z-table, a Z-score of 1.114 corresponds to a probability of 0.8675 to the left, meaning there's a 0.1325 (or 13.35%) chance of a sample mean being greater than 103.5 cm, which rounds to 0.1335.

Heights of Children Entering Kindergarten Are Normally Distributed with a Mean