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).

B. N(μ, 1.30).

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation .

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 and .

So the correct answer is

B. N(μ, 1.30).

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