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The heights of young men follow a Normal distribution with a mean of 175.1 cm and a standard deviation of 7.62 cm. The heights of young women follow a Normal distribution with a mean of 162.1 cm and a standard deviation of 6.35 cm.

Let M = the height of a randomly selected young man

W = the height of a randomly selected young woman

1. Describe the shape, center, and spread of the distribution of M - W.

1. Find the probability that a randomly selected young man is at least 4 centimeters taller than a randomly selected young woman.

Suppose we select independent SRSs of 25 young men and 15 young women.

1. Describe the shape, center, and spread of the sampling distribution ofxM-xW.

1. Find the probability of getting a difference in sample meansxM-xW that's greater than or equal to 4 centimeters.

1. Should we be surprised if the sample mean height for the young women is more than 4 centimeters less than the sample mean height for the young men? Explain.