Question

A study found that the mean amount of time cars spent in​ drive-throughs of a certain​ fast-food restaurant was

157.6157.6

seconds. Assuming​ drive-through times are normally distributed with a standard deviation of

3434

​seconds, complete parts​ (a) through​ (d) below.Click here to view the standard normal distribution table (page 1).

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Click here to view the standard normal distribution table (page 2).

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​(a) What is the probability that a randomly selected car will get through the​ restaurant's drive-through in less than

118118

​seconds?The probability that a randomly selected car will get through the​ restaurant's drive-through in less than

118118

seconds is

nothing.

​(Round to four decimal places as​ needed.)

​(b) What is the probability that a randomly selected car will spend more than

210210

seconds in the​ restaurant's drive-through?The probability that a randomly selected car will spend more than

210210

seconds in the​ restaurant's drive-through is

nothing.

​(Round to four decimal places as​ needed.)

​(c) What proportion of cars spend between

22

and

33

minutes in the​ restaurant's drive-through?The proportion of cars that spend between

22

and

33

minutes in the​ restaurant's drive-through is

nothing.

​(Round to four decimal places as​ needed.)

​(d) Would it be unusual for a car to spend more than

33

minutes in the​ restaurant's drive-through?​ Why?

Answer 1

Solution-A:

X follows normal distribution.

X~N(157.6,34)

P(X<118)

use pnormGC function in R to get the answer.

library(tigerstats)
pnormGC(bound=118,region="below",mean=157.6,sd=34,graph=TRUE)

0.1221

Solution-b:

P(X>210)

pnormGC(bound=210,region="above",mean=157.6,sd=34,graph=TRUE)

P(X>210)=0.0616

Solution-c:

22 min=22*60=1320 seconds

33 min=33*60=1980 seconds

Rcod eis

pnormGC(c(1320,1980),region="between",mean=157.6,sd=34,graph=TRUE)

P(1320<X<1980)=0.0000

Solution-d:

33 min=33*60=1980

P(X>1980)

Rcode:

pnormGC(bound=1980,region="above",mean=157.6,sd=34,graph=TRUE)

=0.0000

P(X>33)=0.0000

since probability =0,chance of happening that is less.

NO

R-screenshot