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Chapter 5: Q. 122 (page 300)

Exponential Probability Between 5:00pm and 6:00pm, cars arrive at Jiffy Lube at the rate of 9cars per hour (0.15car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within tminutes of 5:00pm.

Ft=1-e-0.15t

(a) Determine how many minutes are needed for the probability to reach 50%.

(b) Determine how many minutes are needed for the probability to reach 80%.

Short Answer

Expert verified

(a) Approximately 4.62minlong to reach 50%.

(b) Approximately10.73minlong to reach80%.

Step by step solution

01

Part (a) Step 1. Given information

It is given that Ft=1-e-0.15t.We need to determine how many mins are needed for the probability to reach50%.

02

Step Calculation

50%is 0.5.Substitute 0.5to Ft,

0.5=1-e-0.15t.

0.5-1=-e-0.15t.

-0.5=-e-0.15t.

0.5=e-0.15t.

0.5t=ln0.5.

t=ln0.5-0.15.

t=4.620981204.

鈮�4.62min.

03

Part (b) Step 1. Given information

It is given that Ft=1-e-0.15t.We need to determine how many minutes are needed for the probability to reach80%.

04

Step 2. Calculation

80%is0.8.

Substitute 0.8to Ftin Ft=1-e-0.15t.

0.8=1-e-0.15t.

0.8-1=-e-0.15t.

-0.2=-e-0.15t.

0.2=e-0.15t.

-0.15t=ln0.2.

t=ln0.2-0.15.

t鈮�10.73min.

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