Question

A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 138.6 seconds. Assuming drive-through times are normally distributed with a standard deviation of 30 seconds, complete parts (a) through (d) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected car will get through the restaurant's drive-through in less than 98 seconds? : The probability that a randomly selected car will get through the restaurant's drive-through in less than 98 seconds is (Round to four decimal places as needed.) (b) What is the probability that a randomly selected car will spend more than 190 seconds in the restaurant's drive-through? . The probability that a randomly selected car will spend more than 190 seconds in the restaurant's drive-through is (Round to four decimal places as needed.) (c) What proportion of cars spend between 2 and 3 minutes in the restaurant's drive-through? . The proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is (Round to four decimal places as needed.) (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 (Round to four decimal places as needed.) , so it be unusual, since the probability is than 0.05.

Answer 1

mean = 138.6, standard deviation = 30

$\tiny a) P(x<98)=P(z<\frac{98-138.6}{30}) = P(z<-1.353) = \mathbf{0.088}$

$\tiny b) P(x>190)=P(z>\frac{190-138.6}{30}) = P(z>1.713) = \mathbf{0.0433}$

$\tiny c) P(120<x<180)=P(\frac{120-138.6}{30}<z<\frac{180-138.6}{30}) = P(-0.62<z<1.38) = \mathbf{0.6486}$

180 – 138.6 d)P(1 > 180) = P(:> = —) = P(=> 1.38) = 0.0838 30

The probability that a car spends more than 3 minutes in the restaurants's drive-through is 0.0838 so it not be unusual since the probability is greater than 0.05

Please comment if any doubt. Thank you.