The mean per capita consumption of milk per year is 153 liters with a standard deviation of 27 liters.
If a sample of 90 people is randomly selected, what is the probability that the sample mean would be less than 146.97 liters? Round your answer to four decimal places.
Answer How to enter your answer (opens in new window) 2 Points
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Step 1 ：The problem is asking for the probability that the sample mean is less than 146.97 liters. This is a problem of normal distribution.

Step 2 ：We can use the z-score formula to calculate the z-score for 146.97 liters, and then use the standard normal distribution to find the probability.

Step 3 ：The z-score formula is: \(z = \frac{X - \mu}{\sigma / \sqrt{n}}\) where: \(X\) is the value we are interested in (146.97 liters), \(\mu\) is the mean (153 liters), \(\sigma\) is the standard deviation (27 liters), and \(n\) is the sample size (90).

Step 4 ：After calculating the z-score, we can use the standard normal distribution to find the probability that the z-score is less than the calculated value. This will give us the probability that the sample mean is less than 146.97 liters.

Step 5 ：Final Answer: The probability that the sample mean would be less than 146.97 liters is \(\boxed{0.0171}\).