Respuesta :
Solution:
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) = [tex]_{r}^{n}\textrm{C} p^{r}q^{n - r}[/tex] (1)
P(X ≤ 7) = [tex]_{0}^{20}\textrm{C} (0.20)^{0}(0.80)^{20} +...... + _{7}^{20}\textrm{C} (0.20)^{7}(0.80)^{13}[/tex]
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) = [tex]_{r}^{n}\textrm{C} p^{r}q^{n - r}[/tex] (1)
P(X ≤ 7) = [tex]_{0}^{20}\textrm{C} (0.20)^{0}(0.80)^{20} +...... + _{7}^{20}\textrm{C} (0.20)^{7}(0.80)^{13}[/tex]
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
