Question

Suppose babies born in a large hospital have a mean weight of 3181 grams, and a standard deviation of 526 grams. If 97 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 greater than 53 grams? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 3181

standard deviation = = 526

n = 97

= 3181

= / n = 526 / 97 = 53.4072

P(3128 < < 3234) = P((3128 - 3181) / 53.4072 <( - ) / < (3234 - 3181) / 53.4072))

= 1- P(-0.99 < Z < 0.99)

= 1- ( P(Z < 0.99) - P(Z < -0.99 )) Using z table,

= 1 - (0.8389 - 0.1611)

= 1 - 0.6778

= 0.3222

Probability = 0.3222