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.

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Annette Jolly · Accepted Answer

Final Answer : B, Explanation :  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).

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