Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consumes an amount between 4 and 6 cups?
A)0.5468
B)0.4972
C)0.50
D)none of the options is correct

Question

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consumes an amount between 4 and 6 cups?​
A)0.5468
B)0.4972
C)0.50
D)none of the options is correct

Quizplus · Accepted Answer

To solve this problem, we need to standardize the values using the formula:

z = (X - µ) / σ

where X is the value we want to find the proportion for (in this case, between 4 and 6 cups), µ is the mean (5 cups), and σ is the standard deviation (1.5 cups).

z1 = (4 - 5) / 1.5 = -0.67

z2 = (6 - 5) / 1.5 = 0.67

Now we look up the proportion of values between -0.67 and 0.67 in a standard normal distribution table, which is 0.4972.

Therefore, the proportion of faculty who consume an amount between 4 and 6 cups is 0.4972 or approximately 0.50. The answer is B.

Faculty in the Psychology Department at State University Consume an Average