A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.
To find the percent of data between 4.2 and 5.1, we need to find the Z-scores for both values and then calculate the area between those Z-scores.
First, calculate the Z-score for 4.2 using the formula:
Z = (X - μ) / σ
Z = (4.2 - 5.1) / 0.9
Z = -0.9 / 0.9
Z = -1
Next, calculate the Z-score for 5.1 using the same formula:
Z = (X - μ) / σ
Z = (5.1 - 5.1) / 0.9
Z = 0 / 0.9
Z = 0
Now, we can use a Z-table (or a calculator with a normal distribution function) to find the area between these two Z-scores.
Looking up the Z-score of -1 in the table, we find that the area to the left of -1 is 0.1587 (or 15.87%).
Looking up the Z-score of 0 in the table, we find that the area to the left of 0 is 0.5000 (or 50%).
To find the area between these two Z-scores, we subtract the smaller area from the larger area:
0.5000 - 0.1587 = 0.3413
Therefore, the percent of data between 4.2 and 5.1 is 34.13%.