Step 1

Given information:

Let X be the birth weight of baby.

The average birth weight of bay last year was 7.6 pounds.

The random sample of weights of babies at the hospital \(\displaystyle{\left({n}\right)}={15}\)

Average birth weight of 15 babies is \(\displaystyle{\left(\mu\right)}={7.9}\) pounds.

The birth weight of this is year is normally distributed.

That means, \(\displaystyle{X}\sim{N}{\left({m}{e}{a}{n}={7.9},\sigma\right)}\).

Step 2

In the given scenario, it is given that the distribution of birth weight of this year is normally distributed so it can be said that the distribution of sample means follows normal even if the sample size is less than 30.

In case, the distribution of birth weight of this year is not normal then the sample size must be 30 or more than 30 as per the central limit theorem.

Hence, the correct option is A.

Therefore, Even though the sample size is less than 30, the distribution of sample means will be normal because population data follows normal distribution.

Given information:

Let X be the birth weight of baby.

The average birth weight of bay last year was 7.6 pounds.

The random sample of weights of babies at the hospital \(\displaystyle{\left({n}\right)}={15}\)

Average birth weight of 15 babies is \(\displaystyle{\left(\mu\right)}={7.9}\) pounds.

The birth weight of this is year is normally distributed.

That means, \(\displaystyle{X}\sim{N}{\left({m}{e}{a}{n}={7.9},\sigma\right)}\).

Step 2

In the given scenario, it is given that the distribution of birth weight of this year is normally distributed so it can be said that the distribution of sample means follows normal even if the sample size is less than 30.

In case, the distribution of birth weight of this year is not normal then the sample size must be 30 or more than 30 as per the central limit theorem.

Hence, the correct option is A.

Therefore, Even though the sample size is less than 30, the distribution of sample means will be normal because population data follows normal distribution.