Prob 4 11B:
Use your TI83 (or Excel):
The weights of 9 year old male children are normally distributed population with a mean of 72 pounds and a standard deviation of 14 pounds. Determine the probability that a random sample of 35 such children has an average less than 73 pounds.

Round to four decimal places.

Step 1 ：The problem is asking for the probability that the average weight of a sample of 35 children is less than 73 pounds. This is a problem of normal distribution. We know that the population mean is 72 pounds and the standard deviation is 14 pounds.

Step 2 ：We can use the z-score formula to calculate the z-score for 73 pounds, and then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability. The z-score formula is: \(z = \frac{X - \mu}{\sigma / \sqrt{n}}\) where X is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard deviation, and n is the sample size.

Step 3 ：Substituting the given values into the formula, we get \(z = \frac{73 - 72}{14 / \sqrt{35}}\), which simplifies to \(z = 0.4225771273642583\).

Step 4 ：After calculating the z-score, we can use the CDF to find the probability. The probability that a random sample of 35 such children has an average less than 73 pounds is approximately 0.6637. This means that there is about a 66.37% chance that the average weight of a random sample of 35 children will be less than 73 pounds.

Step 5 ：Final Answer: The final answer is \(\boxed{0.6637}\).