Question

Ahmad and Bryson are in a long-term fitness challenge that involves counting how many calories they consume on a daily basis. Let A = the number of calories Ahmad consumes daily, and B = the number of calories Bryson consumes daily. Based on previous data, they know that A = 2200 calories and 0A = 300 calories. They also know that B = 2400 calories and 0B = 400 calories.

Assume that their daily calorie counts are independent, and let D be the difference between the number of calories they each consume on a randomly selected day (D = B - A). Find the mean and standard deviation of D.

Answer 1

The mean of D, the difference in calories consumed between Bryson and Ahmad, is 200 calories. Since there is no variability mentioned for A or B, we cannot calculate the standard deviation of D without the correct standard deviations of A and B.

Step-by-step explanation:

To find the mean and standard deviation of D, which represents the difference in daily calorie consumption between Ahmad and Bryson, we can use the information given for A and B. Ahmad consumes A = 2200 calories on average and Bryson consumes B = 2400 calories on average.

The mean of D, E(D), is simply the difference between the average calories consumed by Bryson and the average calories consumed by Ahmad, which is E(B) - E(A).

E(D) = E(B) - E(A)

E(D) = 2400 - 2200

E(D) = 200 calories

Since the calorie counts are independent, we can find the standard deviation of D by taking the square root of the sum of the variances of A and B. However, since there is no variability mentioned for A or B, and the values 0A and 0B seem to be irrelevant or possibly typos, we cannot calculate the standard deviation of D without the correct standard deviations of A and B.

If standard deviations were provided, the formula for the standard deviation of D, σD, would be the square root of the sum of the squares of the standard deviations of A and B, assuming they are independent.

σD = √(σA² + σB²)

This formula is based on properties of the standard deviation for independent variables and gives us the standard deviation of the difference between their calorie intakes.