In a study conducted in 1980, researchers calculated the height difference between couples with kids in the UK. They found that the height difference between husband and wife follows a normal distribution with mean 5.6 inches and standard deviation equal to 3.7 inches.

1) What is the difference in height for the middle 68% of the couples in the study?
2) Calculate the percentage of couples in which the man is 5 inches taller than the woman. (you have to use Table B in the book)
3) (harder) Calculate the percentage of couples that have about the same height. Assume that a couple has the same height when the height difference is less than one inch.

given that in a study conducted in 1980, researchers calculated the height difference between couples with kids in the UK. They found that the height difference between husband and wife follows a normal distribution with mean 5.6 inches and standard deviation equal to 3.7 inches.

a) The difference in height for 68% middle of couples in normal distribution is within 1 std dev from the mean

i.e. between (5.6-3.7, 5.6+3.7) = (1.9, 9.3) inches

b) P(x >5) = P(Z>0.6/3.7) = 1-0.5644= 0.4356

Percent = 43.56%

c) P(|x|<1) = P(-1<x<1) = F(1) -F(-1) = 0.0697