Suppose babies born in a large hospital have a mean weight of 3831 grams, and a variance of 108,900. If 65 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would be less than 3882 grams? Round your answer to four decimal places

0.8944

Step-by-step explanation:

We start by calculating the z-score

To calculate the z-score, we shall need the standard deviation

Mathematically, standard deviation is square root of variance

that will be; SD = √108,900 = 330

Formula for z-score is;

x-mean/SD/√n

where n is 65 in this case

z-score = (3882-3831)/330/√65 = 1.25

The probability we want to calculate is;

P( X < 1.25)

we can use the standard normal distribution table for this

Using the table;

P( X < 1.25) = 0.89435 which is 0.8944 to 4. decimal places