Question
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.
Answers
GPT 3.5
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%.
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%.