1. The weight distribution of parcels sent in a certain manner is Normal with me
ID: 3356136 • Letter: 1
Question
1. The weight distribution of parcels sent in a certain manner is Normal with mean value 10 lb and standard deviation 1.75 lb.
a) Provided that the weight of a randomly selected parcel exceeds 8 lb, what is the probability that the parcel weights less than 12.5 lb?
b) The parcel service received new instructions that the surcharge should be taken if the weight exceeds 12.5 lb. What is the probability of surcharge for a randomly selected parcel?
c) Suppose parcels are sent independently one after another. What is the probability that the third parcel with a surcharge is the sixteenth sent?
Explanation / Answer
A) P(8 < x < 12.5) = P((8 - 10)/1.75 < (x - mean)/SD < (12.5 - 10)/1.75
= P(-1.14 < Z < 1.43)
= P(Z < 1.43) - P(Z < -1.14)
= 0.9236 - 0.1271 = 0.7965
B) P(X > 12.5) = P((x - mean)/SD > (12.5 - 10)/1.75
= P(Z > 1.43)
= 1 - P(Z < 1.43)
= 1 - 0.9236 = 0.0764
C) P(X > 16) = P((X - mean)/SD > (16 - 10)/1.75)
= P(Z > 3.43)
= 1 - P(Z < 3.43)
= 1 - 0.9997 = 0.0003
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