A lakeside restaurant found the correlation between the daily temperature and the number of meals they served to be 0.40. On a day when the temperature is two standard deviations above the mean, the number of meals they should plan on serving is __________the mean.
A) 0.4 SD above
B) 2.0 SD above
C) 0.16 SD above
D) 0.8 SD above
E) equal to

Question

Quizplus · Accepted Answer

First, we need to find the correlation coefficient between temperature and the number of meals served, which is 0.40.

Next, we need to find the number of standard deviations above the mean the temperature is on the given day. We are told that it is two standard deviations above the mean.

Finally, we need to use the correlation coefficient and the number of standard deviations to determine the expected number of meals served. We can use the formula:

Expected number of meals = (correlation coefficient) x (number of standard deviations)

Expected number of meals = 0.40 x 2.0 = 0.80 SD above the mean

However, we are told that on this day, the number of meals served should be equal to the mean. This means that the expected number of meals should be zero standard deviations above the mean, which can be achieved by subtracting 0.80 from the actual number of standard deviations above the mean:

Expected number of meals = (correlation coefficient) x (number of standard deviations - 0.80)

Expected number of meals = 0.40 x (2.0 - 0.80) = 0.40 x 1.20 = 0.48 SD above the mean

Therefore, the answer is D) 0.8 SD above.

A Lakeside Restaurant Found the Correlation Between the Daily Temperature