Question

The weights of American newborn babies are normally distributed with a mean of 119.54 oz ( about 7 pounds 8 ounces) and a population standard deviation of .61 oz. A sample of 11 newborn babies is randomly selected from the population.

(a) find the standard error of the sampling distribution. Round your answer to 4 decimal places.

(b) Using your answer to part (a), what is the probability that in a random sample of 11 newborn babies, the mean weight is at most 119.39 oz? Round your answer to 4 decimal places.

(c) using your answer to part (a), what is the probability that the random sample of 11 newborn babies, the mean weight is more than 120.03 oz? round your answer to 4 decimal places.

Answer 1

Solution: It is given here:

(a) find the standard error of the sampling distribution.

Answer: The standard error of the sampling distribution is:

(b) Using your answer to part (a), what is the probability that in a random sample of 11 newborn babies, the mean weight is at most 119.39 oz?

Answer: It is required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that in a random sample of 11 newborn babies, the mean weight is at most 119.39 oz is 0.2073

(c) using your answer to part (a), what is the probability that the random sample of 11 newborn babies, the mean weight is more than 120.03 oz?

Answer: It is required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that the random sample of 11 newborn babies, the mean weight is more than 120.03 oz is 0.0039