The length of pregnancies from conception to birth for a specific breed of horses is, on average, 350 days with a standard deviation of 15 days. Enough medical study has been done on this variable that we know it follows an approximate normal distribution.

Suppose all possible samples of size 50 are drawn from the recorded pregnancy lengths for this horse breed and the mean is found for each resulting sample. Describe the shape and scaling on the graph of the resulting sampling distribution for the sample mean values. Hint: Apply the Central Limit Theorem!

shape: bell

peak:

left scale:

right scale:

Find the probability that the mean number of days of a randomly selected sample of 50 pregnancy lengths of this horse breed is greater than 360 days. Based upon your result, state whether or not it is unusual to randomly select a sample of 50 pregnancy lengths from this horse breed whose sample mean is greater than 60 days, and explain why you chose "unusual" or "not unusual" as your answer.

Find the probability that the mean from a sample of 50 pregnancies from this horse breed will have a mean length somewhere between 345 and 355 days.