Answer to Question #199990 in Statistics and Probability for Amorette

Question #199990

A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 30 minutes and a variance of 25 minutes (squared). Required: a) What is the probability that a randomly selected parcel will take more than 26 minutes to deliver? (2) b) What is the minimum delivery time (minutes) for the 2.5% of parcels with the longest time to deliver? (4


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Expert's answer
2021-05-31T10:39:56-0400

Let X=X= delivery time of parcels: XN(μ,σ2).X\sim N(\mu, \sigma^2).

Given μ=30 min,σ2=25 min2\mu=30\ min, \sigma^2=25\ min^2

a)


P(X>26)=1P(X26)P(X>26)=1-P(X\leq 26)

=1P(Z26305)=1P(Z0.8)=1-P(Z\leq\dfrac{26-30}{5})=1-P(Z\leq-0.8)

0.788147\approx0.788147

b)


P(X<x)=P(Z<x305)=0.025P(X<x)=P(Z<\dfrac{x-30}{5})=0.025

x3051.96\dfrac{x-30}{5}\approx-1.96

x20.2 minx\approx 20.2\ min


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