Please give adequate explanation using math for all parts, thank you. The distri
ID: 3314635 • Letter: P
Question
Please give adequate explanation using math for all parts, thank you.
The distribution of the baggage weights for passengers using a particular airline has a mean of 20 lbs and a standard deviation of 5 lbs. For a random sample of 100 passengers, what is the probability that.. a. the total luggage weight is less than 2080 lbs? Give your answer to 4 decimal places Submit Answer Tries o/s b. the sample mean weight is within 0.5 lb of the overall mean? That is, what is the probability that the sample mean weight is between 19.5 and 20.5 Ibs? Give your answer to 4 decimal places Submit Answer Tries o/s c. The probabilities in parts (a) and (b) are exact. O True False Submit Answer Tries 0/10Explanation / Answer
Solution:- Given that µ = 20, = 5, n = 100
a. E(total) = 100 × 20 = 2,000.
var(total) = 100 × 5^2 = 2500
SD(total) = 50
P(total < 2080) = P(Z < (2080 - 2000)/50) = P(Z < 1.6) = 0.9452
------------------------------(or)-----------------------
Average < 2080/100 = 20.80
P(X < 20.80) = P(Z < (20.80 - 20)/(5/sqrt(100)) = P(Z < 1.6) = 0.9452
b. P(19.5 < X < 20.5) = P((19.5 - 20)/(5/sqrt(100)) < Z < (20.5 - 20)/(5/sqrt(100)) )
= P(-1 < Z < 1)
= 0.6826
c. option A. true