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Mr. Roegner
Statistics
Review for Unit #5 Test
Formulas:
x  
1.a)
x 

n
z
x  x
x
  np
  npq
What does a z-score tell us?
b) In your own words, how do we find a z-score?
2.
Final exam scores are normally distributed with a mean of
83 and a standard deviation of 7. Jimmy’s exam score on
the final is 75. Find the z-score corresponding to this value.
3. Use the standard normal distribution to find P(0<z<1.55).
Shade the indicated region.
4. Use the standard normal distribution to find P(z < -0.85 or
z > 0.85). Shade the indicated region.
5. Use the standard normal
distribution to find P(z>-1.28). Shade the indicated region.
6. The ACT and SAT tests are normally distributed. The mean
scores for the ACT are 21 with a standard deviation of 5,
while SAT has a mean of 1250 with a standard deviation of
120. Bob scored a 24 on the ACT and scored a 1320 on the
SAT. If we use z-scores to compare, which test did he have
a better score on? Explain.
7. Find the z-score with a cumulative area to the left of 0.7307.
8. Assume the starting salaries of elementary school teachers in
the United States are normally distributed with a mean of
$31,000 and a standard deviation of $3,400. What is the
cutoff salary for teachers in the top 15% ?
9. The average number of pounds of red meat a person
consumes each year is 176 with a standard deviation of 21
pounds. If a sample of 50 individuals is randomly selected,
find the probability that the mean of the sample will be more
than 177 pounds.
10. Assume that the heights of men are normally distributed
with a mean of 69.7 inches and a standard deviation of 2.9
inches. If 50 men are randomly selected, find the
probability that they have a mean height greater than 69.9
inches.
11. According to government data, the probability that an adult
was never married is 21%. You randomly select 40 adults
and ask if he or she was ever married. Decide whether you
can use the normal distribution to approximate the binomial
distribution. If so, find the mean and standard deviation. If
not, explain why.
12. According to school data, 14% of the students at LHS are
left-handed. You randomly select 30 students and ask if
they are left-handed. Decide whether you can use the
normal distribution to approximate the binomial distribution.
If so, find the mean and standard deviation. If not, explain
why.
Use the normal distribution to approximate the binomial
distribution for 13 and14.
13. The failure rate in a college statistics class is 19%. In a class
of 30 students, find the probability that
a) more than 6 students fail.
b) exactly 5 students fail.
14. A student answers all 36 questions on a multiple-choice test
by guessing. Each question has four possible answers, only
one of which is correct. Find the probability that the student
gets between 8 and 12 correct, inclusive.