Question

# 4) In order to determine the best-selling style of tennis rackets that are sold in State...

4) In order to determine the best-selling style of tennis rackets that are sold in State College, you have collected data from all sporting goods stores in town. A tennis racket is classified by both its head size and grip size. The Excel sheet “Sales Data Tennis Rackets” in Module 3 contains the data you collected for sales of tennis rackets. Each entry in the Excel sheet represents the sale of one tennis racket. You will have to separate your data and determine the probabilities for specific types of tennis racket that is sold. Assume that the data that has been collected is representative of future sales of different types of rackets and use this information to answer the following questions. (Hint: Use a pivot table to organize this data)

Excel Sheet:

 Customer Number Head Size Grip Size(in) 1 Midsize 4 5/8 2 Oversize 4 1/2 3 Oversize 4 5/8 4 Midsize 4 1/2 5 Midsize 4 3/8 6 Oversize 4 5/8 7 Oversize 4 3/8 8 Midsize 4 1/2 9 Midsize 4 5/8 10 Midsize 4 5/8 11 Midsize 4 5/8 12 Midsize 4 1/2 13 Midsize 4 1/2 14 Midsize 4 3/8 15 Oversize 4 1/2 16 Midsize 4 5/8 17 Midsize 4 3/8 18 Oversize 4 3/8 19 Oversize 4 5/8 20 Oversize 4 1/2 21 Oversize 4 1/2 22 Oversize 4 5/8 23 Midsize 4 1/2 24 Oversize 4 5/8 25 Oversize 4 1/2 26 Midsize 4 5/8 27 Midsize 4 3/8 28 Midsize 4 5/8 29 Midsize 4 1/2 30 Midsize 4 1/2 31 Oversize 4 1/2 32 Oversize 4 5/8 33 Oversize 4 5/8 34 Oversize 4 3/8 35 Oversize 4 3/8 36 Midsize 4 1/2 37 Midsize 4 3/8 38 Midsize 4 5/8 39 Oversize 4 3/8 40 Oversize 4 3/8 41 Midsize 4 1/2 42 Oversize 4 5/8 43 Oversize 4 5/8 44 Oversize 4 1/2 45 Oversize 4 3/8 46 Oversize 4 5/8 47 Midsize 4 3/8 48 Oversize 4 5/8 49 Midsize 4 1/2 50 Oversize 4 5/8 51 Midsize 4 1/2 52 Oversize 4 5/8 53 Midsize 4 1/2 54 Midsize 4 1/2 55 Midsize 4 1/2 56 Midsize 4 5/8 57 Midsize 4 1/2 58 Oversize 4 5/8 59 Oversize 4 3/8 60 Midsize 4 1/2 61 Midsize 4 3/8 62 Midsize 4 5/8 63 Oversize 4 5/8 64 Oversize 4 1/2 65 Oversize 4 1/2 66 Midsize 4 1/2 67 Oversize 4 3/8 68 Oversize 4 5/8 69 Oversize 4 3/8 70 Oversize 4 3/8 71 Oversize 4 3/8 72 Midsize 4 5/8 73 Oversize 4 3/8 74 Oversize 4 5/8 75 Oversize 4 1/2 76 Oversize 4 3/8 77 Midsize 4 3/8 78 Midsize 4 3/8 79 Oversize 4 3/8 80 Oversize 4 5/8 81 Oversize 4 1/2 82 Oversize 4 1/2 83 Midsize 4 5/8 84 Midsize 4 5/8 85 Oversize 4 3/8 86 Midsize 4 1/2 87 Midsize 4 1/2 88 Oversize 4 1/2 89 Oversize 4 1/2 90 Midsize 4 5/8 91 Oversize 4 5/8 92 Oversize 4 3/8 93 Midsize 4 5/8 94 Oversize 4 3/8 95 Oversize 4 1/2 96 Oversize 4 3/8 97 Midsize 4 1/2 98 Oversize 4 3/8 99 Oversize 4 5/8 100 Midsize 4 3/8 101 Oversize 4 5/8 102 Midsize 4 3/8 103 Midsize 4 3/8 104 Oversize 4 1/2 105 Oversize 4 5/8 106 Oversize 4 5/8 107 Midsize 4 1/2 108 Midsize 4 5/8 109 Midsize 4 3/8 110 Oversize 4 3/8 111 Midsize 4 3/8 112 Midsize 4 1/2 113 Oversize 4 3/8 114 Midsize 4 5/8 115 Oversize 4 5/8 116 Oversize 4 3/8 117 Oversize 4 5/8 118 Oversize 4 5/8 119 Oversize 4 3/8 120 Midsize 4 5/8 121 Oversize 4 3/8 122 Oversize 4 3/8 123 Midsize 4 5/8 124 Oversize 4 1/2 125 Midsize 4 1/2 126 Oversize 4 5/8 127 Midsize 4 5/8 128 Midsize 4 1/2 129 Oversize 4 5/8 130 Midsize 4 3/8 131 Midsize 4 3/8 132 Midsize 4 3/8 133 Midsize 4 1/2 134 Oversize 4 3/8 135 Oversize 4 3/8 136 Midsize 4 5/8 137 Oversize 4 3/8 138 Oversize 4 5/8 139 Oversize 4 3/8 140 Midsize 4 5/8 141 Oversize 4 1/2 142 Midsize 4 1/2 143 Oversize 4 5/8 144 Oversize 4 3/8 145 Oversize 4 1/2 146 Midsize 4 5/8 147 Midsize 4 5/8 148 Oversize 4 5/8 149 Midsize 4 5/8 150 Oversize 4 3/8 151 Midsize 4 1/2 152 Midsize 4 5/8 153 Midsize 4 1/2 154 Midsize 4 1/2 155 Oversize 4 1/2 156 Midsize 4 5/8 157 Midsize 4 5/8 158 Oversize 4 1/2 159 Midsize 4 1/2 160 Midsize 4 1/2 161 Oversize 4 1/2 162 Oversize 4 5/8 163 Oversize 4 1/2 164 Midsize 4 3/8 165 Oversize 4 3/8 166 Oversize 4 5/8 167 Midsize 4 1/2 168 Oversize 4 5/8 169 Midsize 4 1/2 170 Midsize 4 5/8 171 Midsize 4 1/2 172 Oversize 4 3/8 173 Oversize 4 3/8 174 Midsize 4 1/2 175 Oversize 4 1/2 176 Oversize 4 1/2 177 Oversize 4 1/2 178 Oversize 4 3/8 179 Oversize 4 3/8 180 Oversize 4 1/2 181 Oversize 4 3/8 182 Midsize 4 1/2 183 Midsize 4 5/8 184 Midsize 4 3/8 185 Midsize 4 1/2 186 Oversize 4 1/2 187 Midsize 4 1/2 188 Oversize 4 5/8 189 Oversize 4 5/8 190 Oversize 4 5/8 191 Oversize 4 3/8 192 Oversize 4 5/8 193 Midsize 4 1/2 194 Oversize 4 1/2 195 Midsize 4 1/2 196 Oversize 4 1/2 197 Midsize 4 3/8 198 Oversize 4 5/8 199 Oversize 4 3/8 200 Oversize 4 5/8

Question 4a:

How many of the rackets with the following style were sold?

Head Size: Oversize                                       Grip Size: 4 1/2

Question 4b:

What is the probability that the racket with the following style will be sold?

Head Size: Oversize                                       Grip Size: 4 5/8

Question 4c:

What is the probability that a racket with a grip size of at least 4-1/2 in. grip was purchased? Determine the probability to 2 decimal places.

Question 4d:

Let A denote the event that a midsize racket was purchased and B denote the event that a racket with a 4-1/2 in. grip was purchased, and C denotes the event that grip size is at least 4-1/2 in. How would you interpret P(A|C)? (CHOOSE THE CORRECT STATEMENT)

 a) The probability of a midsize racket is purchased given that the racket has a grip size of 4-1/2 in.
 b) The probability of a purchased racket has a grip size that is at least 4-1/2 in and it is a midsize racket.
 c) The probability of a purchased racket has a grip size that is 4-1/2 in and it is a midsize racket.
 d) The probability of a purchased racket has a grip size that is at least 4-1/2 in given that it is a midsize racket.
 e) The probability of a midsize racket is purchased given that the racket has a grip size is at least 4-1/2 in.

Question 4e:

Calculate P(A|C) to 2 decimal places.

Question 4f:

What is the notation for the probability that a midsized tennis racket is purchased given that the racket grip size is 4-1/2 in?

 P(B|A)
 P(A|B)
 P(A?B)
 P(A?B)

Question 4g:

Given that a racket is sold with a grip size of 4 ½ in., calculate the probability that the racket sold is a midsized tennis racket is purchased. (4 decimal places).

Question 4h:

Given that a midsize racket is sold, what is the notation of the probability that a midsize tennis racket with racket grip size of 4-1/2 in is purchased? (CHOOSE THE CORRECT ANSWER)

 P(A?B)
 P(A?B)
 P(A|B)
 P(B|A)

Question 4i:

A midsize racket is sold, calculate the probability that a midsize tennis racket with racket grip size of 4-1/2 in is purchased (3 decimal places).