Question

a produce company packages presliced celery and carrots. let x represent the length of a slice of celery, and let y represent the length of a slice of carrot. x and y are independent events. the mean of x is 2.5 inches with a standard deviation of 0.6 inches, and the mean of y is 2.25 inches with a standard deviation of 0.4 inches. what is the mean and standard deviation of the difference, d = x - y?
\\( \mu_d = -0.25 \\) inches and \\( \sigma_d = 0.2 \\) inches
\\( \mu_d = -0.25 \\) inches and \\( \sigma_d = 0.45 \\) inches
\\( \mu_d = 0.25 \\) inches and \\( \sigma_d = 0.52 \\) inches
\\( \mu_d = 0.25 \\) inches and \\( \sigma_d = 0.72 \\) inches

Explanation:

Step1: Calculate mean of D

$\mu_D = \mu_X - \mu_Y = 2.5 - 2.25 = 0.25$ inches

Step2: Calculate variance of D

$\sigma_D^2 = \sigma_X^2 + \sigma_Y^2 = 0.6^2 + 0.4^2 = 0.36 + 0.16 = 0.52$

Step3: Calculate standard deviation of D

$\sigma_D = \sqrt{0.52} \approx 0.72$ inches

Answer:

D. $\mu_D = 0.25$ inches and $\sigma_D = 0.72$ inches