THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a Weight Watchers club.Suppose that the number of times you expect to visit the club in a month is represented by a normally distributed random variable with a mean of 12 and a standard deviation of 2.50.
-The probability is 85% that you average less than how many visits to the club per month over the course of next year?
A)12.75
B)11.50
C)12.50
D)11.75

Question

Quizplus · Accepted Answer

To find the value corresponding to the 85th percentile in a normal distribution, we use the Z-score formula. Given that the mean ($\mu$) is 12 and the standard deviation ($\sigma$) is 2.5, and knowing that the Z-score for 85% in a standard normal distribution table is approximately 1.04, we can set up the equation: $X = \mu + Z\sigma$. Substituting the given values, we get $X = 12 + 1.04(2.5)$, which calculates to approximately 12.75. This means there's an 85% chance of averaging less than 12.75 visits per month.