Final answer:
To find the percentage of data that fall between 40 and 60 in a normal distribution with a mean of 50 and a standard deviation of 5, we can calculate the z-scores for both values and find the area under the normal distribution between these z-scores. The percentage of data between 40 and 60 is approximately 95.45%.
Step-by-step explanation:
To find the percentage of data that fall between 40 and 60, we can use the properties of the normal distribution. Since the mean is 50 and the standard deviation is 5, we can calculate the z-scores for 40 and 60 using the formula: z = (x - μ) / σ. The z-score for 40 is (40 - 50) / 5 = -2, and the z-score for 60 is (60 - 50) / 5 = 2. Then, we can find the area under the normal distribution curve between these two z-scores.
Using a standard normal distribution table or a statistical calculator, we can find that the area between -2 and 2 is approximately 0.9545. This means that approximately 95.45% of the data fall between 40 and 60.