1 The height of 18 yearold men are approximately normally di

1. The height of 18 year-old men are approximately normally distributed, with mean 68 inches and shandard deviation 3 inches (based on information from statistical abstract of the United States, 112 Edition). If a random sample of nine 18 years-old men is selected, what is the probability that the maen height x is greater than 69 inches/

2. The score on the SAT test are normally distributed with mean of 480 and stadard deviation of 85. The test is given to 50 students. What is the probability that the mean X (WITH - ON THE X) of ther scores is between 460 and 500.

3. Consider the normal approximation to the binomial distribution. The owner of a new apartment building must install 25 water heaters. From past experience in other apartment buildings, she knows that Ace is a good brand. An Ace heater is guaranteed for 5 years only, but from her past experience, she knows that the probability it will last 10 years is 25%. What is the probability that 8 or more will last at least 10 years?

Solution

Q1.
Mean ( u ) =68
Standard Deviation ( sd )=3
Number ( n ) = 9
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 69) = (69-68)/3/ Sqrt ( 9 )
= 1/1= 1
= P ( Z >1) From Standard Normal Table
= 0.1587