Question

**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).

Answer #1

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