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The distribution of average wait times in fast food places for a drive-through in a town was approximately normal with μ = 180 seconds and standard deviation σ = 10 seconds. jacob only likes to use the restaurants where the average wait time is in the bottom 10%. what is the maximum average wait time where jacob likes to use the drive-through?

User Snejame
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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.

User Contrapsych
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