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The baggage weights for passengers using a domestic airline are normally distributed with a mean of...

The baggage weights for passengers using a domestic airline are normally distributed with a mean of 22 lbs. and a standard deviation of 4 lbs.

(a) If a passenger is selected at random, what is the probability that the baggage weight of that passenger is more than 30 lbs?

(b) Suppose the limit on total luggage weight is 2250 lbs. If 100 passengers are aboard the airline, what is the probability that their total baggage weight exceeds the limit?

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Math   Statistics-And-Probability   
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Answer #1

Given that, mean (μ) = 22 lbs and standard deviation = 4 lbs

a) We want to find, the probabilitiy that the baggage weight of that passenger is more than 30 lbs.

That is to find, P(X > 30)

Therefore, required probability is 0.0228

b) Total luggage weight is 2250 lbs of 100 passengers.

Sample mean = 2250 / 100 = 22.50 lbs

We want to find,

Therefore, required probability is 0.1056

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