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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?