1. ) Use the data set to answer the following questions :
41 63 56 59 62 62 51
43 55 61 52 68 58 56
56 61 51 54 55 47 53
60 68 48 53 51 62 59
50 58 50 53 55 59 57
a. ) Construct a frequency distribution that has 6 intervals where the first interval begins with 40 and the last interval ends at 70. ( 7 points )
b. ) Form a probability mass function for the frequency distribution in part a. Take the midpoints of your classes as the values that your random variables can take on and define the appropriate probabilities. ( 7 pts )
c. ) Find the mean, variance, and standard deviation for the probability mass function in part b. ( Clearly mark which number answers that question. ) ( 7 points )
2. ) Define 
where 
.
a. ) Is this an example of a probability distribution ? Explain ( Show me ) why or why not. ( 7 points )
b. ) If
this is a probability distribution then find the following percentile :
.
( 8 points )
3. ) Suppose 14 students have tickets for a concert. Three students ( Bob, Jim and Tom ) own cars and will provide transportation to the concert. Bob’s car has room for three passengers ( nondrivers ), while the cars owned by Jim and Tom each has room for four passengers. In how many different ways can 11 passengers be loaded into the cars ? ( 8 points )
4. ) Suppose that there are three male and four female applicants that apply for jobs as cashiers at a discount store. If all the applicants are equally qualified then the three positions will be filled at random. What is the probability that the three hired will all be of the same sex ? ( 8 points )
5. ) Let A,B, and C be such events where 
, 
, and 
.
Find the 
under the following
assumptions :
a. ) If A,B,and C are mutually exclusive events. ( 8 points )
b. ) If A,B, and C are mutually independent events. ( 8 points )
6. ) A person has 3 coins in their pocket. One of the coins has a head on both sides. The other two coins are normal coins. A coin is chosen at random from the pocket and tossed three times.
a. ) Find the probability of obtaining three heads. ( 8 points )
b. ) If a head is obtained on all three tosses, what is the probability that this is the two-headed coin ? ( 8 points )
7. ) Suppose there are 12 songs on a compact disk of which two are your favorites. When using the random button selector on a CD player, each of the 12 selections is played once in random order.
a. ) Find the probability that the second of your two favorites ( which means one of your favorites will have been played before this song ) is the third song that is played. ( 8 points )
b. ) Find the probability that the second of your two favorites ( which means one of your favorites will have been played before this song ) is the sixth song that is played. ( 8 points )