Suppose that the percentage of American drivers who are multitaskers (e.g., talk on cell phones, eat a snack, or text message at the same time they are driving) is approximately 80%. In a random sample of n = 20 drivers, let X equal the number of multitaskers.

(a) How is X distributed?

(b) Give the values of the mean, variance, and standard deviation of X.

(c) Find the following probabilities: (i) P(X = 15),

(ii) P(X > 15), and (iii) P(X ≤ 15).

Solution :

Step 1 of 3:

The percentage of american drivers who are multitaskers is approximately 80%. If a random sample of n=20 multitaskers are taken, and X denote the number of multitaskers. We have to find

(a) distribution of X

(b) mean, variance, standard deviation

(c) The probabilities (i) P(X = 15),

(ii) P(X > 15), and (iii) P(X ≤ 15).