MATH SOLVE

9 months ago

Q:
# An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was = 119.6 ounces. Suppose the standard deviation is known to be σ = 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean μ. Based on the 25 recent birth records, the sampling distribution of the sample mean can be represented by:A. N(μ, 6.5).B. N(μ, 1.30).C. N(119.6, 1.30).D. N(119.6, 6.5).

Accepted Solution

A:

Answer: B. N(μ, 1.30).Step-by-step explanation:The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that:An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was = 119.6 ounces. Suppose the standard deviation is known to be σ = 6.5 ounces.Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean μ. This means that for the sampling distribution, the mean is the mean of the weight of all babies born, so [tex]\mu[/tex] and [tex]s = \frac{6.5}{\sqrt{25}} = 1.30[/tex].So the correct answer is B. N(μ, 1.30).