Question

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 of 5.6 inches and a 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. 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.

Answer 1

Answer:

1) since 68% of the values are within 1 standard deviaiton from the mean

corresponding interval = 5.6 -/+ 3.7 or between 1.90 to 9.30

2)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	5.6
std deviation   =σ=	3.700

probability =P(X>5)=P(Z>(5-5.6)/3.7)

=P(Z>-0.16)

=1-P(Z<-0.16)

=1-0.4364

=0.5636

~ 56.36%

3)

probability = P(-1<X<1)

=P((-1-5.6)/3.7)<Z<(1-5.6)/3.7)

=P(-1.78<Z<-1.24)

=0.1075-0.0375

=0.07

~ 7.00%

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