Toll booths on the New York State thruway are often congested because of the large number of cars waiting to pay. A consultant working for the state concluded that if service times are measured from the time a car stops in line until it leaves, service times are exponentially distributed with a mean of 2.7 minutes. What proportion of cars can get through the toll booth in less than 3 minutes?

Therefore, 67.14% of the cars can get through the toll booth in less than 3 minutes.

Explanation:

A consultant working for the state concluded that if service times are measured from the time a car stops in line until it leaves, service times are exponentially distributed with a mean of 2.7 minutes.

Let X be a random variable. The service time has an exponential distribution with a mean of 2.7 minutes.

Mean = μ = 2.7 minutes

Decay rate = m = 1 /μ

Decay rate = m = 1/2.7

Decay rate = m = 0.371

The cumulative probability distribution function is  given by

Where m is the decay rate and x < 3

So the proportion of cars that can get through the toll booth in less than 3 minutes is

Therefore, 67.14% of the cars can get through the toll booth in less than 3 minutes.

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hi,

henry is an economist and wants to understand the relationship between inflation and consumer spending habits. for his research, he needs the consumer price index for 2014 and the inflation rate. based on the prices of goods given, what will he find to be the cpi and inflation rate for 2014? assume that a consumer’s basket for three consecutive years consists of the following:

you dont privide answer choices.

answer - 15% of a inflatation rate is 15% less in cpi