Question

EXAMPLE 8: Wendy's Drive-Through. Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-throughs. Certainly, the faster the cars get through the drive-through, the more the opportunity for making money. QSR Magazine studied drive- through times for fast-food restaurants and found Wendy's had the best time, with a mean time spent in the drive-through of 138.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 29 seconds, answer the following. (a) Define the variable X, and state its distribution. (d) What proportion of cars spend between 2 and 3 minutes in Wendy's drive-through? (b) What is the probability that a randomly selected car will get through Wendy's drive- through in less than 100 seconds? (c) What is the probability that a randomly selected car will spend more than 160 seconds in Wendy's drive-through? (e) Would it be unusual for a car to spend more than 3 minutes in Wendy's drive-through? Why? (f) The manager at Wendy's told you that the amount of time you spent in the drive-through was faster than 90% of all other customers. How long were you in line?

          EXAMPLE 8: Wendy's Drive-Through.
Fast-food restaurants spend quite a bit of time
studying the amount of time cars spend in their
drive-throughs. Certainly, the faster the cars get
through the drive-through, the more the opportunity
for making money. QSR Magazine studied drive-
through times for fast-food restaurants and found
Wendy's had the best time, with a mean time spent
in the drive-through of 138.5 seconds. Assuming
drive-through times are normally distributed with a
standard deviation of 29 seconds, answer the
following.
(a) Define the variable X, and state its distribution.
(d) What proportion of cars spend between 2 and 3
minutes in Wendy's drive-through?
(b) What is the probability that a randomly selected
car will get through Wendy's drive- through in less
than 100 seconds?
(c) What is the probability that a randomly selected
car will spend more than 160 seconds in Wendy's
drive-through?
(e) Would it be unusual for a car to spend more than 3
minutes in Wendy's drive-through? Why?
(f) The manager at Wendy's told you that the amount
of time you spent in the drive-through was faster than
90% of all other customers. How long were you in
line?

Show more…

EXAMPLE 8: Wendy's Drive-Through.
Fast-food restaurants spend quite a bit of time
studying the amount of time cars spend in their
drive-throughs. Certainly, the faster the cars get
through the drive-through, the more the opportunity
for making money. QSR Magazine studied drive-
through times for fast-food restaurants and found
Wendy's had the best time, with a mean time spent
in the drive-through of 138.5 seconds. Assuming
drive-through times are normally distributed with a
standard deviation of 29 seconds, answer the
following.
(a) Define the variable X, and state its distribution.
(d) What proportion of cars spend between 2 and 3
minutes in Wendy's drive-through?
(b) What is the probability that a randomly selected
car will get through Wendy's drive- through in less
than 100 seconds?
(c) What is the probability that a randomly selected
car will spend more than 160 seconds in Wendy's
drive-through?
(e) Would it be unusual for a car to spend more than 3
minutes in Wendy's drive-through? Why?
(f) The manager at Wendy's told you that the amount
of time you spent in the drive-through was faster than
90% of all other customers. How long were you in
line?

Added by James K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

09/21/2022

Step 1

- X represents the time a car spends in Wendy's drive-through. - X follows a normal distribution with a mean of 138.5 seconds and a standard deviation of 29 seconds. Show more…

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Transcript

00:01 Hi, i'm david and i'm here to hear you happy i'm seeing the question.

00:03 In the question here we are going to discuss about the normal distribution.

00:07 Let me remind you that if the x that follows by the normal with the mean and the standard deviation and if we tend the x minus the mean of the standard deviation we attend the standard normal.

00:19 In the question here we have the x that will be the time spent in the time span in the trial rule it will follow by the normal when the mean equal to the 1 .30 and the standard deviation equal to the 29 seconds.

00:37 Now in the question a asked us to define the random probable x and state the distribution.

00:45 So we did here already but let me write again.

00:48 X will be the time span in the drive rule and it will follow by the normal would the mean equal to 138 .5.

01:13 And the standard division equal to the 29.

01:17 And for the question b, we want to find the probability that the x here will be less than 100.

01:26 Now to find this probability and if you convert the x here into the z, and to do it, i need to apply this formula.

01:35 And we will take the 100, we minus the mean 138 .5, depending by the standard deviation.

01:41 And if we compute we have the z smaller than we have the minus 38 .5 by 29 and then we got equal to the minus 1 .3 28 and then to compute this one i use the normal distribution and this one will be smaller than the 1 .3 28 then we get equal to the 0 .09 21 i go to the four decimal places and for the question c once you find the probability that will be more than 160 so x will be greater than the 160 again i can put the x here into the z and to do it i will change the 160 and minus the mean over the standard deviation then we have the z will be greater than 160 minus 130 8 .5 divided by the 29 equal to the zepone 7 for 1 and if we will compare this one we will have it will be the zero from 7 4 1 we'll get equal to the zepon 2 to 94 and for the question d want to find the probability that it will be between 2 and 3 minutes so x will be 2 minutes, it will be the 120, and 3 minutes equal to the 180...

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