Question

According to a 2017 Wired magazine article, 40% of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (Wired magazine website). Suppose we randomly select 50 received e-mails.

a. What is the expected number of these e-mails that are tracked?
b. What are the variance (to the nearest whole number) and standard deviation (to 3 decimals) for the number of these e-mails that are tracked?
c. Variance Standard deviation?

Answer 1

The expected number of e-mails that are tracked is 20. The variance is 12 and the standard deviation is approximately 3.464.

Step-by-step explanation:

a. To find the expected number of e-mails that are tracked, we multiply the probability of an e-mail being tracked (40%) by the total number of e-mails received (50):

Expected number of tracked e-mails = Probability of tracking x Number of e-mails = 0.4 x 50 = 20

b. To find the variance and standard deviation for the number of e-mails that are tracked, we use the formula:

Variance = Probability of tracking x (1 - Probability of tracking) x Number of e-mails = 0.4 x 0.6 x 50 = 12

Standard deviation = Square root of variance = √12 ≈ 3.464

c. Variance measures the spread or variability of the data. Standard deviation is the square root of the variance and gives us a measure of the average amount by which the data deviate from the mean.