Question

he mean cost of domestic airfares in the United States rose to an all-time high of $375 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $555 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $260 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $310 and $500 (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)
$  or - Select your answer -morelessItem 5

Answer 1

a)

Here, μ = 375, σ = 120 and x = 555. We need to compute P(X >= 555). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (555 - 375)/120 = 1.5

Therefore,
P(X >= 555) = P(z <= (555 - 375)/120)
= P(z >= 1.5)
= 1 - 0.9332 = 0.0668

b)

Here, μ = 375, σ = 120 and x = 260. We need to compute P(X <= 260). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (260 - 375)/120 = -0.96

Therefore,
P(X <= 260) = P(z <= (260 - 375)/120)
= P(z <= -0.96)
= 0.1685

c)

Here, μ = 375, σ = 120, x1 = 310 and x2 = 500. We need to compute P(310<= X <= 500). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (310 - 375)/120 = -0.54
z2 = (500 - 375)/120 = 1.04

Therefore, we get
P(310 <= X <= 500) = P((500 - 375)/120) <= z <= (500 - 375)/120)
= P(-0.54 <= z <= 1.04) = P(z <= 1.04) - P(z <= -0.54)
= 0.8508 - 0.2946
= 0.5562

d)

z value at 3% = 1.88

z = (x - mean)/sigma

1.88 = (x - 375)/120

x = 120 *1.88 + 375
x = 601

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