A physicalfitness association is including the mile run in i

A physical-fitness association is including the mile run in its secondary school fitness test for boys. The time for this event for boys in secondary school is approximately normally distributed with a mean of 450 seconds and a standard deviation of 40 seconds. If the association wants to designate the fastest 10% as \"excellent\" what time should the association set for this criterion? The Tall Americans Club (TAC) is a social club for tall people. To join the club, women must be at least 72 inches tall and men must be at least 75 inches tall. The National Health Survey reports that the mean height of women in the U. S. is 63 inches with a standard deviation of 2. 5 inches. The mean height of men in the U. S. is 69 inches with a standard deviation of 2. 8 inches. We can reasonably assume that heights are normally distributed. What percent of the adult female population of the U. S. could qualify for membership to TAC? What percent of the adult male population of the U. S. could qualify for membership in to TAC? What should we change the height of the females so that there is the same percentage in the TAC from both genders?

Solution

3.
P ( Z < x ) = 0.9
Value of z to the cumulative probability of 0.9 from normal table is 1.282
P( x-u/s.d < x - 450/40 ) = 0.9
That is, ( x - 450/40 ) = 1.28
--> x = 1.28 * 40 + 450 = 501.28