Math 227 Exam # 2 Last Name: First Name:
Read CAREFULLY & Box your answers
For calculations: set up the problem first and then use your calculator
You can only use a calculator – NOT any other electronic device. If you do, you’ll Fail. 52 pts
Use the following data for #1-2
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
1) Calculate the following measures (6pts)
a) Mean d) Interquartile range
b) Median e) Population Standard deviation
c) Mode f) Sample Variance
2) Construct a Boxplot – and clearly label the values for the 5-number summary. (6pts)
3) Circle the formula for permutations: nPr (1pt)
𝑛!
(𝑛 − 𝑟)!
𝑟!
(𝑟 − 𝑛)!
𝑛!
(𝑟 − 𝑛)!
4) Circle the formula for combinations: nCr (1pt)
𝑟!
(𝑟 − 𝑛)! 𝑟!
𝑛!
(𝑛 − 𝑟)! 𝑟!
𝑟!
(𝑟 − 𝑛)! 𝑛!
5) Evaluate 8P4 (2pts) 6) Evaluate 8C4 (2pts)
Problems 7-9: 2 pts each
7) If a person is randomly selected, find the probability that his/her birthday is NOT in May. Ignore leap years.
8) From a deck of cards, find P(10 or Diamond). (Recall: Four suits. Each suit is from Ace to King)
9) What is the complement of the answer of the previous problem?
10) A tourist in France wants to visit 7 out of 10 different cities. How many possible specific travel routes can
be made? (3pts)
11) ‘Mean’ is another way of saying ‘Average’. Another way of saying is ‘__________________ Value’ (1pt)
12) The number of golf balls ordered by customers of a pro shop has the following probability distribution.
Find the mean and the standard deviation of this probability distribution. (4pts)
𝒙 𝒑(𝒙) 3 0.14 6 0.36 9 0.36
12 0.04 15 0.10
For problems 13,14,15, round your answer to the nearest hundredth. (2pts each)
13) Find the standard deviation for the binomial distribution given the following values: 𝑛 = 503 𝑝 = 0.7
14) Find the mean for the binomial distribution given the following values: 𝑛 = 676 𝑝 = 0.7
15) Find the standard deviation for the binomial distribution given the following values: 𝑛 = 38 𝑝 = 0.4
16) The following table contains data from a study of two airlines which fly to Small Town, USA.
Number of flights on time Number of flights late
Podunk Airlines 33 6
Upstate Airlines 43 5
a) If one of the flights is randomly selected, find the probability that it is a Podunk Airline or a flight which was
on time. (3pts)
b) If one of the flights is randomly selected, find the probability that it is an Upstate Airline or a Podunk
Airlines that was late. (3pts)
17) The following table contains data from a study of accurate orders at several fast food restaurants.
McDonald’s Burger King Wendy’s Taco Bell
Order Accurate 329 264 249 145
Order Not Accurate 33 54 31 13
a) If one order is randomly selected, find the probability of getting food that is NOT from Wendy’s. (3pts)
b) If one order is randomly selected, find the probability of getting food from McDonald’s or an order that is
accurate. (3pts)
18) The following is NOT a probability distribution. Why? (Write a clear short explanation.) (3pts)
𝒙 𝑷(𝒙) 0 0.109 1 0.208 2 0.246 3 0.159 4 0.096 5 0.228
