1. Assume that the provided data represent a sample of customers who visited the

Question

1. Assume that the provided data represent a sample of customers who visited the Pelican Store in a day.

a. What is the probability that the age of customers was between 28 and 45 years.

b. For the type of payment, what is the probability that less than of 45% customers paid by the Proprietary Card?

Customer Type of Customer Items Net Sales Method of Payment Gender Marital Status Age 1 Regular 1 39.50 Discover Male Married 32 2 Promotional 1 102.40 Proprietary Card Female Married 36 3 Regular 1 22.50 Proprietary Card Female Married 32 4 Promotional 5 100.40 Proprietary Card Female Married 28 5 Regular 2 54.00 MasterCard Female Married 34 6 Regular 1 44.50 MasterCard Female Married 44 7 Promotional 2 78.00 Proprietary Card Female Married 30 8 Regular 1 22.50 Visa Female Married 40 9 Promotional 2 56.52 Proprietary Card Female Married 46 10 Regular 1 44.50 Proprietary Card Female Married 36 11 Regular 1 29.50 Proprietary Card Female Married 48 12 Promotional 1 31.60 Proprietary Card Female Married 40 13 Promotional 9 160.40 Visa Female Married 40 14 Promotional 2 64.50 Visa Female Married 46 15 Regular 1 49.50 Visa Male Single 24 16 Promotional 2 71.40 Proprietary Card Male Single 36 17 Promotional 3 94.00 Proprietary Card Female Single 22 18 Regular 3 54.50 Discover Female Married 40 19 Promotional 2 38.50 MasterCard Female Married 32 20 Promotional 6 44.80 Proprietary Card Female Married 56 21 Promotional 1 31.60 Proprietary Card Female Single 28 22 Promotional 4 70.82 Proprietary Card Female Married 38 23 Promotional 7 266.00 American Express Female Married 50 24 Regular 2 74.00 Proprietary Card Female Married 42 25 Promotional 2 39.50 Visa Male Married 48 26 Promotional 1 30.02 Proprietary Card Female Married 60 27 Regular 1 44.50 Proprietary Card Female Married 54 28 Promotional 5 192.80 Proprietary Card Female Single 42 29 Promotional 3 71.20 Proprietary Card Female Married 32 30 Promotional 1 18.00 Proprietary Card Female Married 70 31 Promotional 2 63.20 MasterCard Female Married 28 32 Regular 1 75.00 Proprietary Card Female Married 52 33 Promotional 3 63.20 Proprietary Card Female Married 44 34 Regular 1 40.00 Proprietary Card Female Married 34 35 Promotional 5 105.50 MasterCard Female Married 56 36 Regular 1 29.50 MasterCard Male Single 36 37 Regular 2 102.50 Visa Female Single 42 38 Promotional 6 117.50 Proprietary Card Female Married 50 39 Promotional 5 13.23 Proprietary Card Female Married 44 40 Regular 2 52.50 Proprietary Card Female Married 58 41 Promotional 13 198.80 Proprietary Card Female Married 42 42 Promotional 4 19.50 Visa Female Married 46 43 Regular 2 123.50 Proprietary Card Female Married 48 44 Promotional 1 62.40 Proprietary Card Female Married 54 45 Promotional 2 23.80 Proprietary Card Female Married 38 46 Promotional 2 39.60 Proprietary Card Female Married 60 47 Regular 1 25.00 MasterCard Female Married 46 48 Promotional 3 63.64 Proprietary Card Female Married 30 49 Promotional 1 14.82 Proprietary Card Female Married 32 50 Promotional 9 145.20 MasterCard Female Married 46 51 Promotional 6 176.62 Proprietary Card Female Married 38 52 Promotional 5 118.80 Proprietary Card Male Married 68 53 Regular 1 58.00 Discover Female Single 78 54 Regular 2 74.00 Visa Female Single 20 55 Regular 2 49.50 MasterCard Female Married 32 56 Promotional 3 141.60 Proprietary Card Female Married 38 57 Promotional 6 123.10 Proprietary Card Female Married 54 58 Promotional 2 80.40 Proprietary Card Female Married 48 59 Promotional 4 65.20 MasterCard Female Married 46 60 Promotional 4 113.00 Proprietary Card Female Single 50 61 Promotional 1 108.80 Proprietary Card Female Married 46 62 Promotional 3 59.91 Proprietary Card Female Single 30 63 Promotional 5 53.60 Proprietary Card Female Married 54 64 Promotional 1 31.60 Proprietary Card Female Single 42 65 Promotional 2 49.50 Proprietary Card Female Married 48 66 Promotional 1 39.60 Proprietary Card Female Married 62 67 Promotional 2 59.50 Proprietary Card Female Married 34 68 Promotional 5 146.80 Proprietary Card Female Married 28 69 Promotional 2 47.20 Proprietary Card Male Married 46 70 Promotional 8 95.05 Proprietary Card Female Married 54 71 Promotional 5 155.32 Proprietary Card Female Married 30 72 Promotional 4 58.00 MasterCard Female Married 32 73 Regular 1 69.00 Proprietary Card Female Single 22 74 Promotional 2 46.50 Proprietary Card Female Married 32 75 Promotional 2 45.22 Proprietary Card Female Married 74 76 Promotional 4 84.74 Proprietary Card Female Married 62 77 Regular 2 39.00 Proprietary Card Female Married 42 78 Promotional 4 111.14 Proprietary Card Female Married 28 79 Promotional 3 86.80 Proprietary Card Female Married 38 80 Regular 2 89.00 Discover Female Married 54 81 Promotional 2 78.00 MasterCard Female Married 68 82 Promotional 6 53.20 Proprietary Card Female Single 30 83 Promotional 4 58.50 Visa Female Married 36 84 Promotional 3 46.00 Proprietary Card Female Married 44 85 Regular 2 37.50 Visa Female Married 44 86 Promotional 1 20.80 Proprietary Card Female Married 62 87 Regular 6 144.00 MasterCard Female Single 48 88 Regular 4 107.00 Proprietary Card Female Married 36 89 Promotional 1 31.60 Proprietary Card Female Single 20 90 Promotional 6 57.60 Proprietary Card Female Married 42 91 Promotional 4 95.20 Proprietary Card Female Married 54 92 Promotional 1 22.42 Proprietary Card Female Married 54 93 Regular 5 159.75 Proprietary Card Female Married 72 94 Promotional 17 229.50 Proprietary Card Female Married 30 95 Regular 3 66.00 American Express Female Married 46 96 Regular 1 39.50 MasterCard Female Married 44 97 Promotional 9 253.00 Proprietary Card Female Married 30 98 Promotional 10 287.59 Proprietary Card Female Married 52 99 Promotional 2 47.60 Proprietary Card Female Married 30 100 Promotional 1 28.44 Proprietary Card Female Married 44 101 Regular 1 39.50 Discover Male Married 32 102 Promotional 1 102.40 Proprietary Card Female Married 36 103 Regular 1 22.50 Proprietary Card Female Married 32 104 Promotional 5 100.40 Proprietary Card Female Married 28 105 Regular 2 54.00 MasterCard Female Married 34 106 Regular 1 44.50 MasterCard Female Married 44 107 Promotional 2 78.00 Proprietary Card Female Married 30 108 Regular 1 22.50 Visa Female Married 40 109 Promotional 2 56.52 Proprietary Card Female Married 46 110 Regular 1 44.50 Proprietary Card Female Married 36 111 Regular 1 29.50 Proprietary Card Female Married 48 112 Promotional 1 31.60 Proprietary Card Female Married 40 113 Promotional 9 160.40 Visa Female Married 40 114 Promotional 2 64.50 Visa Female Married 46 115 Regular 1 49.50 Visa Male Single 24 116 Promotional 2 71.40 Proprietary Card Male Single 36 117 Promotional 3 94.00 Proprietary Card Female Single 22 118 Regular 3 54.50 Discover Female Married 40 119 Promotional 2 38.50 MasterCard Female Married 32 120 Promotional 6 44.80 Proprietary Card Female Married 56 121 Promotional 1 31.60 Proprietary Card Female Single 28 122 Promotional 4 70.82 Proprietary Card Female Married 38 123 Promotional 7 266.00 American Express Female Married 50 124 Regular 2 74.00 Proprietary Card Female Married 42 125 Promotional 2 39.50 Visa Male Married 48 126 Promotional 1 30.02 Proprietary Card Female Married 60 127 Regular 1 44.50 Proprietary Card Female Married 54 128 Promotional 5 192.80 Proprietary Card Female Single 42 129 Promotional 3 71.20 Proprietary Card Female Married 32 130 Promotional 1 18.00 Proprietary Card Female Married 70 131 Promotional 2 63.20 MasterCard Female Married 28 132 Regular 1 75.00 Proprietary Card Female Married 52 133 Promotional 3 63.20 Proprietary Card Female Married 44 134 Regular 1 40.00 Proprietary Card Female Married 34 135 Promotional 5 105.50 MasterCard Female Married 56 136 Regular 1 29.50 MasterCard Male Single 36 137 Regular 2 102.50 Visa Female Single 42 138 Promotional 6 117.50 Proprietary Card Female Married 50 139 Promotional 5 13.23 Proprietary Card Female Married 44 140 Regular 2 52.50 Proprietary Card Female Married 58 141 Promotional 13 198.80 Proprietary Card Female Married 42 142 Promotional 4 19.50 Visa Female Married 46 143 Regular 2 123.50 Proprietary Card Female Married 48 144 Promotional 1 62.40 Proprietary Card Female Married 54 145 Promotional 2 23.80 Proprietary Card Female Married 38 146 Promotional 2 39.60 Proprietary Card Female Married 60 147 Regular 1 25.00 MasterCard Female Married 46 148 Promotional 3 63.64 Proprietary Card Female Married 30 149 Promotional 1 14.82 Proprietary Card Female Married 32 150 Promotional 9 145.20 MasterCard Female Married 46 151 Promotional 6 176.62 Proprietary Card Female Married 38 152 Promotional 5 118.80 Proprietary Card Male Married 68 153 Regular 1 58.00 Discover Female Single 78 154 Regular 2 74.00 Visa Female Single 20 155 Regular 2 49.50 MasterCard Female Married 32 156 Promotional 3 141.60 Proprietary Card Female Married 38 157 Promotional 6 123.10 Proprietary Card Female Married 54 158 Promotional 2 80.40 Proprietary Card Female Married 48 159 Promotional 4 65.20 MasterCard Female Married 46 160 Promotional 4 113.00 Proprietary Card Female Single 50 161 Promotional 1 108.80 Proprietary Card Female Married 46 162 Promotional 3 59.91 Proprietary Card Female Single 30 163 Promotional 5 53.60 Proprietary Card Female Married 54 164 Promotional 1 31.60 Proprietary Card Female Single 42 165 Promotional 2 49.50 Proprietary Card Female Married 48 166 Promotional 1 39.60 Proprietary Card Female Married 62 167 Promotional 2 59.50 Proprietary Card Female Married 34 168 Promotional 5 146.80 Proprietary Card Female Married 28 169 Promotional 2 47.20 Proprietary Card Male Married 46 170 Promotional 8 95.05 Proprietary Card Female Married 54 171 Promotional 5 155.32 Proprietary Card Female Married 30 172 Promotional 4 58.00 MasterCard Female Married 32 173 Regular 1 69.00 Proprietary Card Female Single 22 174 Promotional 2 46.50 Proprietary Card Female Married 32 175 Promotional 2 45.22 Proprietary Card Female Married 74 176 Promotional 4 84.74 Proprietary Card Female Married 62 177 Regular 2 39.00 Proprietary Card Female Married 42 178 Promotional 4 111.14 Proprietary Card Female Married 28 179 Promotional 3 86.80 Proprietary Card Female Married 38 180 Regular 2 89.00 Discover Female Married 54 181 Promotional 2 78.00 MasterCard Female Married 68 182 Promotional 6 53.20 Proprietary Card Female Single 30 183 Promotional 4 58.50 Visa Female Married 36 184 Promotional 3 46.00 Proprietary Card Female Married 44 185 Regular 2 37.50 Visa Female Married 44 186 Promotional 1 20.80 Proprietary Card Female Married 62 187 Regular 6 144.00 MasterCard Female Single 48 188 Regular 4 107.00 Proprietary Card Female Married 36 189 Promotional 1 31.60 Proprietary Card Female Single 20 190 Promotional 6 57.60 Proprietary Card Female Married 42 191 Promotional 4 95.20 Proprietary Card Female Married 54 192 Promotional 1 22.42 Proprietary Card Female Married 54 193 Regular 5 159.75 Proprietary Card Female Married 72 194 Promotional 17 229.50 Proprietary Card Female Married 30 195 Regular 3 66.00 American Express Female Married 46 196 Regular 1 39.50 MasterCard Female Married 44 197 Promotional 9 253.00 Proprietary Card Female Married 30 198 Promotional 10 287.59 Proprietary Card Female Married 52 199 Promotional 2 47.60 Proprietary Card Female Married 30 200 Promotional 1 28.44 Proprietary Card Female Married 44

Explanation / Answer

a. What is the probability that the age of customers was between 28 and 45 years.

Solution:

From given data set, we have following information:

Number of customers between 28 and 45 years = 106

Total number of customers = 200

Required probability = Number of customers between 28 and 45 years / Total number of customers

Required probability = 106/200

Required probability = 0.53

b. For the type of payment, what is the probability that less than of 45% customers paid by the Proprietary Card?

Solution:

From given data set, we have following information:

Number of customers who paid by using Proprietary Card = 140

Total number of customers = 200

Probability for using Proprietary Card = 140/200 = 0.70

We have to find probability that less than of 45% of customers paid by Proprietary Card.

45% of 200 customers = 90

We have to find P(X<90) given n = 200, p = 0.70

We have to use normal approximation to binomial distribution.

q = 1 – p = 1 – 0.70 = 0.30

n*p = 200*0.70 = 140

n*q = 200*0.30 = 60

n*p and n*q > 5, so we can use normal approximation.

Mean = n*p = 200*0.70 = 140

SD = sqrt(n*p*q) = sqrt(200*0.70*0.30) = 6.480741

We have to find P(X<90)

By subtracting continuity correction factor 0.5, we have to find P(X<89.5)

Z = (X – mean) / SD

Z = (89.5 – 140) / 6.480741

Z = -7.79232

P(Z<-7.79232) = 0.0000

Required probability = 0.0000

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