Answer:
Step-by-step explanation:
Given that the management decides to evaluate the satisfaction surveys of its next 40 customers.
Fine if favourable number is between 22 and 26,
Dissolved if fewer than 22 report favourably
Let X be the number of persons who report favourably.
X is binomial with n =40 and p = 0.70
a. Probability that the dealer will be fined
=![P(22\leq X\leq 26)\\=P(22)+P(23)+...P(26)\\=40C22 (0.7)^{22}(0.3)^{18} +40C23 (0.7)^{23}(0.3)^{17} +...40C26 (0.7)^{26}(0.3)^{14} \\\\=0.2968-0.0148\\=0.2820](https://tex.z-dn.net/?f=P%2822%5Cleq%20X%5Cleq%2026%29%5C%5C%3DP%2822%29%2BP%2823%29%2B...P%2826%29%5C%5C%3D40C22%20%280.7%29%5E%7B22%7D%280.3%29%5E%7B18%7D%20%20%2B40C23%20%280.7%29%5E%7B23%7D%280.3%29%5E%7B17%7D%20%2B...40C26%20%280.7%29%5E%7B26%7D%280.3%29%5E%7B14%7D%20%5C%5C%5C%5C%3D0.2968-0.0148%5C%5C%3D0.2820)
b. the probability that the dealership will be dissolved
= ![P(X](https://tex.z-dn.net/?f=P%28X%3C22%29%5C%5C%3D0.0148)