Question

The number of homeruns scored by teams in the Brooksfielf baseball league are normally distributed and have a mean of 94 and a standard deviation of 8. What percentage of the teams have scored more than 102 home runs?​

Answer 1

Answer:

16%

Step-by-step explanation:

The Empirical Rule claims that 68% of the values in a normal distribution are within 1 standard deviation of the mean, 95% are within 2 standard deviations, and 99.7% are within 3. Using this here, we can see that 102 is exactly 1 standard deviation from the mean, as 94 + 8 * 1 = 102.

We also know that a normal distribution is symmetric, meaning that there is an equal distribution on both sides of the mean. Therefore, we can say that 50% of the values are above the mean. Next, 68% of values are within 1 standard deviation of the mean, so here, we can say that 34% of values are between the mean and 1 positive standard deviation of the mean. We want to find how many values are greater than 1 standard deviation of the mean. This is equal to (total amount of values greater than the mean) - (total amount of values greater than the mean but not greater than 1 standard deviation of the mean) = 50% - 34% = 16%