Question

The Atlanta Braves baseball team has a mean batting average of 250 with a standard deviation of 20. Assume the batting averages are approximately normally distributed.

What percent of Braves players fall between 230 and 270?

Answer 1

Approximately 68.3% of Atlanta Braves players have batting averages between 230 and 270, as this range falls within one standard deviation of the mean (250) in a normal distribution.

Step-by-step explanation:

The question you've asked involves finding the percentage of Atlanta Braves players with batting averages between 230 and 270, given that the mean batting average is 250 and the standard deviation is 20. To solve this, we will use properties of the normal distribution.

First, we need to calculate the z-scores for the batting averages of 230 and 270:

Z-score for 230 = (230 - 250) / 20 = -1

Z-score for 270 = (270 - 250) / 20 = 1

Now, we can look up these z-scores on a standard normal distribution table or use a z-score calculator. Typically, a z-score of -1 corresponds to the 15.85th percentile, and a z-score of 1 corresponds to the 84.15th percentile. To find the percentage of players between these two scores, we subtract the smaller percentile from the larger one:

84.15% - 15.85% = 68.3%

Therefore, approximately 68.3% of Braves players have batting averages that fall between 230 and 270.

Answer 2

68 %

Step-by-step explanation:

Since we have our mean x = 250 and standard deviation σ = 20, we need to find how many standard deviations away the values 230 and 270 are.

Note x - σ = 250 - 20 = 230 and x + σ = 250 + 20 = 270

The values are one standard deviation away.

So, the values between 230 and 270 lie in the range x - σ to x + σ.

Since the batting averages are approximately normally distributed and for a normal distribution, 68 % of the values lie in the range x - σ to x + σ.

So, 68 % of Braves players fall between 230 and 270.