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Normal Prob. Distributions – Review 7.1 – 7.4
1. Know the important properties of a normal curve
a.
b.
c.
d.
2. Sketch a normal curve with mean 12 and standard deviation 2.
3. What percentage of the area under the normal curve lies
a. to the right of μ?
b. between μ and μ + σ?
c. between μ – 3σ and μ + 3σ?
4. The yearly wheat yield per acre on a particular farm is normally distributed
with mean μ = 30 bushels and standard deviation σ = 3 bushels.
a. Sketch this normal curve
b. Shade the area under the curve that represents the probability
that an acre will yield between 27 and 33 bushels.
5. Assuming the heights of college women are normally distributed, with mean 68
in. and a standard deviation 2 in., answer the following questions.
A. What percentage of women are shorter than 68 in.?
B. What percentage of women are between 64 in. and 72 in.?
C. What percentage of women are between 62 in. and 74 in.?
D. What percentage of women are taller than 70 in.?
6. What is the standard normal distribution?
7. A student computed that it takes an average (mean) of 15 minutes with a
standard deviation of 3 minutes to drive from home, park the car, and walk to an
early morning class.
a. One day it 24 minutes to get to class. Find the z value.
b. Another day it took only 14 minutes for the student to get to class.
Find the z value.
8. Jim’s z score on a college entrance exam is 1.7. If the raw scores have a mean
of 450 and a standard deviation of 60 points, what is his raw score?
9. Sue got a 55 on the last statistics test. If the μ = 65 and σ = 5, find her z
score.
10. Find the area over the indicated intervals.
a. To the left of z = 1.0
b. To the left of z = -.55
c. To the right of z = 0.45
d. Between z = -1.40 and z = 2.03
11. Assume that x has a normal distribution with the specified mean and standard
deviation. Find the indicated probabilities.
a. P2  x  8;
  5;   2
b. P60  x  70;
  50;   15
12. Find the z value described
a. Find z such that 3% of the standard normal curve lies to the left of z
b. Find z such that 3% of the standard normal curve lies to the right of z
c. Find z such that 85% of the standard normal curve lies between –z and z
13. A certain watch company shows that their watches have an average life of 30
months. The standard deviation of watch lifetimes is 5 months and the
distribution is normal.
a. If the company guarantees a full refund on any defective watch for 18
months after purchase, what percentage of total production will the
company expect to replace?
b. If the company does not want to make refunds on more than 10% of the
watches it makes, how long should the guarantee period be (to the
nearest month)?
14. Define:
a. Sampling distribution
b. Parameter
c. Statistic
d. Population
e. Sample