Question

9. Fill in the blank. The heights of adult men in America are normally distributed, with a mean of 69.1 inches and standard deviation of 2.65 inches It is sometimes said that women don't like to dance with shorter men. To get a dancing partner, a 6-foot-tall woman draws from a hat the name of an adult American male. The probability that he will be as tall as she is (Give your answer rounded to a whole number.) e 6.2 gives the information needed to cakculate the percentile from the core Percentile from 2-Score Percentile core 0.00 53,98 7.93 61.79 2.7 2.5 -2.3 -2.1 1.9 0.1 0.2 0.62 1.07 69.13 72.57 75.80 78.81 1.59 84.13 86.43 88.49 90.32 91.92 1.0 1.6 1.5 1.2 1.3 14 1,5 16 668 1.3 11.51 13.57 15.87 18.41 21.19 24.20 94.52 95.54 6.41 97.13 7.73 98.21 98.61 98.93 9.18 99,38 99.53 99,65 9.8 1.9 2.1 3o.xs 38.21 0.5 46.02 0.00 -0.1

Answer 1

Here, mean = 69.1 , s =2.65

x = 6 foot = 12 *6 = 72 inches

P(x> 72)
= P(z >(x - mean)/s)
= P(z> (72 - 69.1)/2.65)
= P(z > 1.09)
= 0.1369
= 13.69%
=14%