Question

an amateur bowler calculated his bowling average for the season. if the data are normally distributed, about how many of his 50 games were within 1 standard deviation of the mean? (1 point)
options: 50, 40, 17, 34

Explanation:

Step1: Recall Empirical Rule

In a normal distribution, about 68% of data lies within 1 standard deviation of the mean.

Step2: Calculate Number of Games

Total games = 50. Find 68% of 50: $0.68\times50 = 34$. Wait, no, wait—wait, the empirical rule: within 1 standard deviation (μ - σ to μ + σ) is about 68%? Wait, no, wait, maybe I misremembered. Wait, no, the empirical rule (68 - 95 - 99.7) says that approximately 68% of the data is within 1 standard deviation of the mean, 95% within 2, 99.7% within 3. Wait, but 68% of 50: $0.68\times50 = 34$? But wait, maybe the options—wait, the options include 34? Wait, the options are (I can see 58, 40, 17, 34? Wait, maybe I misread. Wait, the problem: "about how many of his 50 games were within 1 standard deviation of the mean". So using empirical rule, 68% of data is within 1σ of μ. So 68% of 50: $0.68\times50 = 34$? Wait, but maybe the options—wait, the options given: let's check the options again. The options are (from the image, I can see): 58, 40, 17, 34? Wait, no, maybe the original problem's options—wait, maybe I made a mistake. Wait, no, 68% of 50 is 34? Wait, but wait, maybe the empirical rule is 68%? Wait, no, wait, actually, the correct percentage for within 1 standard deviation is approximately 68%, so 68% of 50 is 34. Wait, but let's recalculate: 50 * 0.68 = 34. So the answer should be 34? Wait, but maybe the options—wait, the user's image shows options, and one of them is 34? Wait, the last option is 34? So step by step:

1. Recall empirical rule: ~68% data within 1σ of mean.
2. Calculate 68% of 50: 0.68 * 50 = 34.

Answer:

34 (assuming the option with 34 is the correct one, likely the last option).