Answer:
a) The probability that a randomly selected car will get through the restaurant's drive-through in less than 105 seconds is 5.59%.
b) The probability that a randomly selected car will spend more than 195 seconds in the restaurant's drive-through is 12.71%
Step-by-step explanation:
Normally distributed problems can be solved by the z-score formula:
On a normaly distributed set with mean and standard deviation
, the z-score of a value X is given by:
After we find the value of Z, we look into the z-score table and find the equivalent p-value of this score. This is the probability that a score will be LOWER than the value of X.
A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 157.4 seconds. This means that
Assuming drive-through times are normally distributed with a standard deviation of 33 seconds. This means that .
(a) What is the probability that a randomly selected car will get through the restaurant's drive-through in less than 105 seconds?
This probability is the pvalue of the zscore of
has a pvalue of .0559. This means that there is a 5.59% probability that a randomly selected car will get through the restaurant's drive-through in less than 105 seconds,
(b) What is the probability that a randomly selected car will spend more than 195 seconds in the restaurant's drive-through?
This is 1 subtracted by the pvalue of the zscore of .
has a pvalue of .87286. This means that there is a 87.286% probability that a randomly selected car will get through the restaurant's drive-through in less than 195 seconds.
So the probability that a randomly selected car will spend more than 195 seconds in the restaurant's drive through is