A normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points. Use the empirical rule for normal distributions to estimate the probability that in a randomly selected game the player scored less than 26 points.
- Provide the final answer as a percent rounded to one decimal place.

Step 1 ：A normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points. We are asked to estimate the probability that in a randomly selected game the player scored less than 26 points.

Step 2 ：We can use the empirical rule for normal distributions, also known as the 68-95-99.7 rule, to solve this problem. This rule states that for a normal distribution, almost all values lie within 3 standard deviations of the mean. More specifically, 68% of the data falls within the first standard deviation, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 3 ：In this case, the mean is 20 points and the standard deviation is 3 points. So, scoring less than 26 points is within two standard deviations from the mean (20 + 2*3 = 26). According to the empirical rule, this covers approximately 95% of the data.

Step 4 ：So, the probability that the player scores less than 26 points in a randomly selected game is approximately 95%.

Step 5 ：However, this is an approximation. To get a more accurate result, we would need to use the cumulative distribution function (CDF) for a normal distribution. The CDF at a point x gives the probability that a random variable is less than or equal to x.

Step 6 ：Using the CDF, we find that the probability is approximately 0.9772498680518208, or 97.7%.

Step 7 ：Final Answer: The probability that the player scores less than 26 points in a randomly selected game is approximately \(\boxed{97.7\%}\).