Question

A study found that the mean amount of time cars spent in​ drive-throughs of a certain​ fast-food restaurant was 132.9 seconds. Assuming​ drive-through times are normally distributed with a standard deviation of 30 seconds, complete parts​ (a) through​ (d) below. (Round to 4 decimal places as needed)

(a) What is the probability that a randomly selected car will get through the​ restaurant's drive-through in less than 98 ​seconds?

​(b) What is the probability that a randomly selected car will spend more than 172 seconds in the​ restaurant's drive-through?

​(c) What proportion of cars spend between 2 and 3 minutes in the​ restaurant's drive-through?

​(d) Would it be unusual for a car to spend more than 3 minutes in the​ restaurant's drive-through?​ Why?

The probability that a car spends more than 3 minutes in the​ restaurant's drive-through is (BLANK), so it (would OR would not) be​ unusual, since the probability is (less OR greater) than 0.05.

Answer 1

Here in this scenario we calculated the step by step probability of all Questions using Standerd normal distribution as below,

Here we covered the min in second that means 1min = 60 sec.

(a) the probability that a randomly selected car will get through the​ restaurant's drive-through in less than 98 ​seconds is 0.1223.

​(b) The probability that a randomly selected car will spend more than 172 seconds in the​ restaurant's drive-through is 0.0962.

.

​(c) What proportion of cars spend between 2 and 3 minutes in the​ restaurant's drive-through that means between 120 sec and 180 sec is 0.6082.

​(d) the probability a car to spend more than 3 minutes in the​ restaurant's drive-through is 0.0582.

Yes it is not unusual

So it would not be unusual because the probability is greater than 0.05.

Thank you.