In a certain city, the mean price of a two litter bottle of soda is $1.50 and th

Question

In a certain city, the mean price of a two litter 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 litter 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 ten 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 ten people spent is at least $25?

Explanation / Answer

a) expected total amount = 1.50*6 + 3.80*4 =24.2

SD = 0.50

b) P( x> 25 )   P( z > 25 - 24.2 / 0.50 )

P( z > 1.6 ) = 0.0548

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