Each year a company must send officials to China and to France. Assume airfare p

Question

Each year a company must send officials to China and to France. Assume airfare prices to China and France vary independently. Past experience has shown that tickets to China have a mean price of $1,000, with as standard deviation of $150, while the mean airfare to France is $500, with a standard deviation of $110. Assume the company is going to send one official to China and one to France Find the mean cost for airfare to send both officials. Find the standard deviation of the cost to send both officials. Round to one decimal as needed Budgets are tight and the company feels it might need to postpone trips if the total airfare budget exceeds $1,700. What's the chance they will need to postpone trips? Round to four decimals as needed. Instead of one to each country the company decides to cancel any China trips and instead send 3 to France. What's the chance the purchase of these tickets will exceed the $1,700 budget? Note: The company purchases 3 tickets at the same time for the same price for the same trip. In other words, multiply 3 times the cost of one ticket. Three tickets are NOT purchased separately. Round to four decimals as needed.

Explanation / Answer

a)
mean = 1000 + 500 = 1500

b)
std. dev. = sqrt(150^2 + 110^2) = 186.0107

c)
P(X > 1700)
= P(z > (1700 - 1500)/186.0107)
= P(z > 1.0752)
= 0.1411

d)
mean = 3*500 = 1500
std. dev. = 110 * sqrt(3) = 190.5256

P(X > 1700)
= P(z > (1700 - 1500)/190.5256)
= P(z > 1.0497)
= 0.1469

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