Suppose babies born in a large hospital have a mean weight of 4022 grams, and a standard deviation of 266 grams. If 53 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by more than 45 grams?

Question

Juliet Brock

Mathematics

3 December, 09:50

Suppose babies born in a large hospital have a mean weight of 4022 grams, and a standard deviation of 266 grams. If 53 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by more than 45 grams?

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Answers (1)

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Moyer · Answer 1

Answer: 0.866

Step-by-step explanation:

Mean = 4022

SD = 266

We are looking for the probability of samples 45g differ than the mean. Hence 2 probability combination:

X>4067 and X<3977

Calculate for Z we'll get Z = 0.16917 and - 0.161917

Using Z formula we can find P (Z=0.17) = 0.433

Since both probability will occupy the same area, total probability is 0.433x2 = 0.866