Ch. 10
MM Trig.
Name:___________________________
Statistics Review 3
Find the mean, median, and mode on problem 1:
1. The skill drill scores for the Level 16 Test:
50, 13, 85, 74, 75, 92, 77, 68, 71, 98, 90, 82, 67, 91, 75
2. Draw a box-and-whisker plot for the Level 16 test scores; label all features:
50, 13, 85, 74, 75, 92, 77, 68, 71, 98, 90, 82, 67, 91, 75
Find the variance and standard deviation for the following data:
3. The following are the weights, in pounds, of 20 members of the football team:
218, 184, 200, 155, 131, 195, 215, 188, 194, 223, 251, 203, 200, 152, 143, 192, 218, 185, 199, 220
4. The final exam scores for Algebra 3-4:
64, 98, 100, 24, 89, 92, 78, 68, 71, 98, 95, 82, 69, 100, 76, 49, 96, 105, 19, 91, 90, 79, 66, 73, 96, 97, 80
State whether or not the distribution is a probability distribution.
6.
X
2
3
6
7
9
P X  1/3 1/15 1/15 1/5 1/3
Ch. 10 rev, MM Trig.
Pg. 2
7. A box contains 2 red balls and one blue ones. A ball is pulled until a blue one is drawn. Construct a probability
distribution for the number of pulls, and then calculate the expected number of pulls when doing this activity.
8. A box contains three quarters, two dimes, one nickle, and five pennies. Construct a probability distribution for the
data using a random variable representing the value of one random coin taken from the box.
9. A ski resort loses $70,000 per season when there is insufficient snowfall and makes $250,000 profit when there is
sufficient snowfall. The probability of it snowing at least 75 inches (i.e. sufficient snowfall) is 40%. Let X be the
random variable representing the profit in a given season. Find the expected Value of X.
10. A box contains ten $1 bills, three $2 bills, three $5 bills, one $10 bill, and three $100 bills. A person is charged
$25 to select one bill. Find the expectation. Is the game fair?
11.A student takes a 10-question, multiple choice test with answer choices “a” through “d.” If the student guesses on
every problem, find the probability that his ten question examination has exactly 7 answer choices marked “c”.
Ch. 10 rev, MM Trig.
Pg. 3
16 An independent market research firm found that 90% of Americans like reality television shows. If a random
sample of 10 Americans is selected, find these probabilities.
a) Exactly 6 people will like reality television shows.
b) At most five people will like reality television shows.
c) At least five people will like reality television shows.
d) More than one person will like reality television shows.
Given that Z is normally distributed with mean 0 and standard deviation 1, find the following probabilities:
17. P(0  Z  1.2) =
18. P( Z  .71)
19. P( Z  2)
20. If the mean weight of college freshman males is 189 pounds, and the standard deviation is 15 pounds, find the
probability that a college freshman weighs less than 160 pounds. Assume a normal distribution.
Find the value of z . Assume Z is normally distributed with   0 and   1
20. If PZ  z   0.8
21. If P(0<Z<z)=.412
22. PZ  z   .35
23.The Toyonda automobile gets an average 35.0 miles per gallon in the city. The standard deviation is 5 miles per
gallon. Assume the variable is normally distributed. Find the probability that on any given day, the car will get less
than 20 miles per gallon when driven in the city.
Ch. 10 rev, MM Trig.
Pg. 4
24. The average “sitting time” for burgers at a local fast food restaurant is 1 minute, with a standard deviation of .5
minutes. If burgers that sit for two minutes are thrown away, how many burgers does this particular fast food chain
throw away if it makes 2000 burgers a day? Assume the variable is Normally distributed.
25. The mean lifetime of a wristwatch is 18 months, with a standard deviation of 2 months. If the distribution is
normal, for how many months should a guarantee be if the manufacturer does not want to exchange more than 5% of
the watches? Assume the variable is normally distributed.
26. A test is given in which the scores are normally distributed and the mean of the scores was 72 points. If a score of
70 is a passing grade, and 65% of the students in the class passed, what was the standard deviation of the test scores?