Answer: To find the proportion of values between 87 and 140, you first need to calculate the z-scores for these values. The formula for calculating the z-score is:
z = (x - mean) / standard deviation
Where x is the value you want to convert to a z-score, the mean is the mean of the distribution, and the standard deviation is the standard deviation of the distribution.
For x = 87,
z = (87 - 109.72) / 24
z = -0.95
For x = 140,
z = (140 - 109.72) / 24
z = 1.26
Now, you can use a standard normal distribution table to find the proportion of values between -0.95 and 1.26.
Looking at the table, the area to the left of -0.95 is 0.1711 and the area to the left of 1.26 is 0.8962. Therefore, the proportion of values between 87 and 140 is:
0.8962 - 0.1711 = 0.7251
So, approximately 72.51% of the values are between 87 and 140.
Step-by-step explanation:
