Practice Chapters 6
1. Find the value of Z
such that 0.10 of the area under the curve lies to the right of the Z.
2. Find the value of Z
such that 0.05 of the area under the curve lies to the left of the Z.
3. The random variable X has a normal distribution with a mean of 200 and a standard deviation of 25.
a. Find probability that X is between 160 & 220
b. Find probability that X is greater than 240
c. Find probability that X is less than 150
d. Find probability that X is greater than 200
e. Find probability that X is less than 200
f. Find probability that X is between 100 & 300
g. Find probability that X is between 210 & 250
4. What percentage of the values in a normal distribution are:
a. More than 1 standard deviation away from the mean?
b. Greater than the mean, but less than 2 standard deviations above the mean?
5. Convert to standard normal distribution (indicate z-value)
a. µ=65 & σ=20; x=40
b. µ=15 & σ=2; x=19
c. µ=12,000 & σ=2000; x=10,750
6. The mean is 166.9 minutes and the standard deviation is 55.4 minutes. What percentage was:
a. < 3 hours
b. >2 hours
c. >2.5 hours & <3.5 hours
d. <2.5 hours or >3.5 hours
7. What z-value has an area:
a. of 0.9803 to its left
b. of 95th percentile
c. of 0.9706 to its right
d. between –z and z is 0.99
8. Normal distribution has mean of 95.0 and standard deviation of 8.8. What is the value of the random variable X with an area to its right equal to 0.0526?