SOLUTION: Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 2 inches. (a) What is the probability that an 18-year-

Algebra ->  Parallelograms -> SOLUTION: Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 2 inches. (a) What is the probability that an 18-year-      Log On


   

Question 378075: Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 2 inches.
(a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall?
(b) If a random sample of sixteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

a)probability that an 18-year-old man selected at random is between 68 and 70 inches tall

 z+=+blue%28x+-+mu%29%2Fblue%28sigma%29

 z+=+blue%2870+-+69%29%2Fblue%282%29= .5  NORMSDIST(.5)  = .6915

z+=+blue%2868+-+69%29%2Fblue%282%29= -.5  NORMSDIST(-.5) = .3085

P(-.5 < z > .5) = .6915 - .3085 = .3829  Or 39.29%



b)random sample of sixteen 18-year-old men is selected

test statistic = z+=blue+%28X+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29

 z= 1/(2/4)  =  2  NORMSDIST(2)  = .6915 = .9773

 z = -1/(2/4)= -2  NORMSDIST(-2)  = .6915 = .0228

P(-2 < z > 2) = .9973 - .0228 = .9545  Or 95.45%