Suppose that the national mean weight for a three-year-old girl is 30 pounds with a standard deviation of 5 pounds.A pediatric office takes a random sample of 100 three-year-old girls,records their weights,and finds the mean.Describe the sampling distribution model of this mean.
A)Binom(30,5)
B)N(30,0.5)
C)N(30,0.05)
D)N(30,5)
E)There is not enough information to describe the distribution.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean for a sufficiently large sample size (n ≥ 30) from a population with a known mean (μ) and standard deviation (σ) is normally distributed as N(μ, σ/√n). Here, μ = 30, σ = 5, and n = 100, so the standard deviation of the sampling distribution (σ/√n) is 5/√100 = 0.5, leading to a distribution of N(30, 0.5).

Suppose That the National Mean Weight for a Three-Year-Old Girl