Question

1. Let Z be a standard normal random variable. Find…

a. Pr (Z ≥ -0.78) b. Pr(-0.82  Z  1.31)

2. A random variable X is normally distributed with mean ? = 25.5 and standard deviation ? .0= 3.25.

Find Pr(23.03 ≤ ?? ≤ 29.14)

3. The math SAT is scaled so that the mean score is 500 and the standard deviation is 100.
Assuming scores are normally distributed, find the probability that a randomly selected student
scores

a. higher than 645 on the test. b. at most 475 on the test   

4. Adult male heights are a normal random variable with mean 69 inches and a standard deviation of 3 inches. Find the height, to the nearest inch, for which only 8 percent of adult males are taller (i.e. find the 92nd percentile)

Answer 1

1 ) Let ,

a. Now ,

; From standard normal distribution table

b.

; From standard normal distribution table

2 ) Let ,

Now ,

; From standard normal distribution table

3) Let ,

a.

; From standard normal distribution table

Therefore , the probability that the randomly selected student score is higher than 645 in the test is 0.0735

b.

; From standard normal distribution table

Therefore , the probability that the randomly selected student score is at most 475 on the test is 0.4013

4 ) Let ,

We have ,

............(I)

Also , From standard normal distribution table , ..............(II)

From (I) and(II) , we get ,

Therefore , the 92nd percentile is 73.20 inches.