5.20 In a certain city, the mean price of a two-liter bottle of soda is $1.50 an

Question

5.20 In a certain city, the mean price of a two-liter bottle of soda is $1.50 and the standard deviation is $0.20 at various grocery stores. The mean price of one gallon of milk is $3.80 and the standard deviation is $0.30. Ten tourists came to the city together. They separately went to randomly chosen grocery stores, and each person bought one item. Six of them bought two-liter bottles of soda, and each of the remaining four bought one gallon of milk. a. What is the expected total amount of money that the 10 people spent? b. If the prices of individual items are independent and normally distributed, what is the probability that the total amount of money the 10 people spent is at least $25?

Explanation / Answer

here let X is price of 2 liter bottle and Y is that of one gallon of milk,

a) expected total amount of money that the 10 people spent =6E(X)+4*E(Y)=6*1.5+4*3.8 =24.2

b) std deviation of total amount =((6*0.20)2+(4*0.3)2)1/2 =1.697

therefore probability that the total amount of money the 10 people spent is at least $25

=P(X>25) =1-P(X<25) =1-P(Z<(25-24.2)/1.697)=1-P(Z<0.4714)=1-0.6813 =0.3187

please revert for any clarification required,

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