Question

Suppose babies born in a large hospital have a mean weight of 3361 grams, and a variance of 245,025 f 117 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 44 grams? Round your answer to four decimal places. Show supporting work including an appropriately shaded sketch of the normal curve described in the scenario. Answer How to Enter) 10 Points Tables keypad Prev Next

Answer 1

Let X is a random variable shows the weight of baby. Here X has normal distribution with following parameters

u=3361,0 = V245025 = 495

The z-score for is

Y = μ - 44

μ σ/νη μ - 44 -μ 495/117 = -0.96

The z-score for is

Τ = μ +44

T- + 44 - MI on 495/117 = 0.96

Using z table, the required probability is

Plicu - 44) +PT>+44) = P(Z <-0.96) + P(Z > 0.96) = P(Z < -0.96) + 1 - P(Z <= 0.96) = 0.1685 +1 -0.8315 = 0.3370

Answer 0.3370

Following is the curve: