At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 26 minutes and a standard deviation of 4 minutes. What is the probability that a randomly selected customer will have to wait between 29 minutes and 34 minutes, to the nearest thousandth?
To find the probability that a randomly selected customer will have to wait between 29 minutes and 34 minutes, we need to calculate the z-scores for each of these times and then find the area under the normal distribution curve between these two z-scores.
First, we find the z-score for 29 minutes:
z = (29 - 26) / 4 = 0.75
Next, we find the z-score for 34 minutes:
z = (34 - 26) / 4 = 2.00
Now, we use a z-table or a calculator to find the area under the curve between these two z-scores. The area is the probability:
P(0.75 ≤ Z ≤ 2.00) = 0.4772 - 0.7734 = 0.2958
Therefore, the probability that a randomly selected customer will have to wait between 29 minutes and 34 minutes is approximately 0.296 (or 29.6%).