Question

What is the probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean?( length of pregnancies of a certain animal are approximately normally distributed with mean of 295 days and standard deviation of 15 days)​

Answer 1

Answer:

0.9864

Step-by-step explanation:

The average sample mean is 295, and the standard deviation is:

σ = 15 / √17

σ = 3.64

The z-scores are:

z = (x − μ) / σ

z₁ = (-9) / 3.64

z₁ = -2.47

z₂ = (9) / 3.64

z₂ = 2.47

So the probability is:

P(-2.47 < Z < 2.47) = P(Z < 2.47) − P(Z < -2.47)

P(-2.47 < Z < 2.47) = 0.9932 − 0.0068

P(-2.47 < Z < 2.47) = 0.9864