Final answer:
To find Jacob's maximum acceptable average wait time which is in the bottom 10% of fast food place drive-throughs, we calculate the z-score corresponding to the 10th percentile and find it to be approximately -1.28. Applying this z-score to the normal distribution with a given mean of 180 seconds and standard deviation of 10 seconds, Jacob's maximum average wait time is 167.2 seconds.
Step-by-step explanation:
The student wants to know the maximum average wait time at the bottom 10% of fast food places for a drive-through, when the wait times are normally distributed with a mean (μ) of 180 seconds and standard deviation (σ) of 10 seconds. To find this, we need to determine the z-score that corresponds to the bottom 10% of the distribution. Looking up this value in a standard normal distribution table, or using a calculator for the inverse normal distribution function, we find that the z-score for the 10th percentile is approximately -1.28.
To convert the z-score back to the wait time in seconds, we use the formula:
X = μ + (z * σ)
Where X is the wait time that corresponds to Jacob's maximum acceptable average wait time. Plugging in the values gives us:
X = 180 + (-1.28 * 10) = 180 - 12.8 = 167.2 seconds
Therefore, the maximum average wait time where Jacob likes to use the drive-through is 167.2 seconds.