At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 46 minutes and a standard deviation of 4 minutes. What is the probability that a randomly selected customer will have to wait less than 41 minutes, to the nearest thousandth?
To find the probability that a randomly selected customer will have to wait less than 41 minutes, we need to calculate the z-score and then use the standard normal distribution table.
First, calculate the z-score:
z = (X - μ) / σ
z = (41 - 46) / 4
z = -1.25
Next, look up the z-score in the standard normal distribution table. The table will give you the probability of a z-score less than -1.25.
From the standard normal distribution table, the probability of a z-score less than -1.25 is approximately 0.1056.
Therefore, the probability that a randomly selected customer will have to wait less than 41 minutes is 0.1056 (rounded to the nearest thousandth).