Session 177
How NORMAL are we EXPECTED to be?
CMC South Conference 2015
Example 1
Student AStudent BStudent C
607760
757960
808080
8582100
10082100
A. Find the standard deviation for Student A.
Student A______
60
75
80
85
100
B. Find the standard deviation for Student B.
Example 2
Suppose the heights of adult males have a mean of 69.5 inches and a standard deviation of 2.5 inches.
Mr. McInerney is 73 inches tall.
A. What proportion of adult males are less than 73 inches tall?
B. What proportion of adult males are less than 68 inches tall?
C. What proportion of adult males are greater than 75 inches tall?
D. What proportion of adult males are between 68 inches tall and 73 inches tall?
E. Joakim Noah of the Chicago Bulls is 6 foot 11 inches tall. How many standard deviations away from
the mean is Noah?
Example 3
Weights of full-term newborn babies are approximately normally distributed with a mean of 7.72 pounds and a standard deviation of 1.32 pounds.
A. In January, 2014, a California mother delivered a 15.125 pound baby boy. How many standard
deviations above the mean was his birth weight?
B. What proportion of full-term newborns weigh between 6 and 8 pounds? Show all work and a picture
of the normal probability curve.
Example 4
The distribution of weights of 9-ounce bags of Bubba’s Potato Chips is claimed to be approximately normal with a mean µ = 9.12 ounces and a standard deviation σ = 0.05 ounce.
A. What percent of bags would be at least 9.1 ounces?
B. What percent of bags would weigh between 9.05 and 9.17 ounces?
C. What is the maximum weight for the lightest 15% of bags?
D. Would a bag that weighed less than 9 ounces cause you to question Bubba’s claim? Why?
Example 5
For a particular pitcher, based on previous games played, it is determined that his probability of throwing X strikes in a particular at-bat are as follows:
XP(X)
00.03
10.27
20.54
30.16
Example 6
You pay $5 to play a game. You roll a die. If you get a 1 or 2, you lose. If you get a 3 or 4, you get $3 back. If you get a 5 or 6, you get $10 back.
A. Find the expected profit for one play of this game. Should you play this game?
B. Assuming all other payouts stay the same, what payout would have to be awarded for rolling a 5 or 6 to make this game fair?
Example 7
You are going to play a game where you roll a fair, six-sided die. If you roll an even number, you lose the $5 you paid to play this game. If you roll an odd number, you will receive a number of dollars back equivalent to the value the die shows times 2.
a) What is the expected amount of money you will receive back in one play of this game?
b) What is your expected profit in one play of this game?
Example 8
The graph below displays the relative frequency distribution for X, the total number of dogs and cats owned per household, for the households in a large suburban area.
A. According to a local law, each household in this area is prohibited from owning more than 3 of these
pets. If a household in this area is selected at random, what is the probability that the selected
household will be in violation of this law?
B. You know that your friend’s family has at least 3 dogs & cats, but you cannot recall exactly how
many. Given what you know, what is the probability that your friend’s family has 7 cats?
C. Again, you know that your friend’s family has at least 3 dogs & cats. Which statement would you feel
more comfortable making: “My friend has 3 dogs & cats” or “My friend has 5 or 6 dogs & cats”?
Explain.
D. Find the expected number of dogs/cats per household for someone in this suburban community.