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The drive-thru times at Tim Horton’s are normally distributed with µ = 138.5 seconds and σ...

The drive-thru times at Tim Horton’s are normally distributed with µ = 138.5 seconds and σ = 29 seconds.

(a) What is the probability that a randomly selected car will get through the drive-thru in less than 100 seconds?

(b) What is the probability that a randomly selected car will spend more than 160 seconds in the drive-thru?

(c) What proportion of cars spend between 2 and 3 minutes in the drive-thru?

(d) Would it be unusual for a car to spend more than 3 minutes in the drive-thru? Why?

Solutions

Expert Solution

According to the given question, the drive-thru times at Tim Horton’s are normally distributed with mean

seconds and standard deviation

seconds.

(a) The probability that a randomly selected car will get through the drive-thru in less than 100 seconds is .

Explanation:

The area under the standard normal curve is determined from a standard normal table as:

The area is shaded in black as:

(b) The probability that a randomly selected car will spend more than 160 seconds in the drive-thru is .

Explanation:

The area over the standard normal curve from is determined from a standard normal table as:

The area is shaded in black as:

(c) The proportion of cars spend between 2 and 3 minutes in the drive-thru is   or 66.2 %.

Explanation:

The area under the standard normal curve from and is determined from a standard normal table as:

The area is shaded in black as:

(d) The probability that a car to spend more than 3 minutes in the drive-thru is

Explanation:

The area over the standard normal curve from is determined from a standard normal table as:

The area is shaded in black as

As the probability that a car to spend more than 3 minutes in the drive-thru is is more than , therefore this is not unusual.

milcah answered 1 year ago
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