Question

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 7 of the calls involve a fax message?

Answer 1

Total no. of incoming calls, n = 20

Probability of incoming calls with fax messages, p = 20% = 0.20

q = (1 - p) = 0.80

(a) Now, let 'r' be the no. of incoming calls with fax messages, then by Binomial distribution of probability mass function:

P(X = r) =
`_(r)^(n)\textrm{C} p^(r)q^(n - r)` (1)

P(X ≤ 7) =
`_(0)^(20)\textrm{C} (0.20)^(0)(0.80)^(20) +...... + _(7)^(20)\textrm{C} (0.20)^(7)(0.80)^(13)`

P(X ≤ 7) = 0.0115 +........+ 0.0545

Total no. of incoming calls, n = 20

Probability of incoming calls with fax messages, p = 20% = 0.20

q = (1 - p) = 0.80

(a) Now, let 'r' be the no. of incoming calls with fax messages, then by Binomial distribution of probability mass function:

P(X = r) =
`_(r)^(n)\textrm{C} p^(r)q^(n - r)` (1)

P(X ≤ 7) =
`_(0)^(20)\textrm{C} (0.20)^(0)(0.80)^(20) +...... + _(7)^(20)\textrm{C} (0.20)^(7)(0.80)^(13)`

P(X ≤ 7) = 0.0115 + 0.0545

P(X ≤ 7) = 0.9689

probability that atmost 7 of the calls are with fax is 0.9689