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A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 40 customers. The dealer will be fined if the number of customers who report favorably is between 22 and 26. The dealership will be dissolved if fewer than 22 report favorably. It is known that 70% of the dealer�s customers report favorably on satisfaction surveys.





a.
What is the probability that the dealer will be fined



b.
What is the probability that the dealership will be dissolved?

Respuesta :

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

=[tex]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[/tex]

b.  the probability that the dealership will be dissolved

= [tex]P(X<22)\\=0.0148[/tex]

fichoh

Using the binomial principle, the probability that dealer is fined and the probability that dealership will be dissolved is 0.2820 and 0.01478 respectively.

Recall :

  • P(x = x) = nCx * p^x * q^(n-x)

  • p = probability of success ; = 0.70

  • q = 1 - 0.7 = 0.30

A.)

Probability that dealer will be fined :

P(22≤ x ≤26) = [P( x =22) + p(x = 23) + p(x = 24) + p(x = 25) + p(x = 26)]

Using a binomial probability calculator :

P(22≤ x ≤26) = 0.01717 +0.03136 + 0.05183 + 0.0774 + 0.10419

P(22≤ x ≤26) = 0.2820

B.)

Probability that dealership will be dissolved :

P(x < 22) = p(x=21)+p(x=20)+...+p(x=0)

P(x < 22) = 0.01478

Therefore, the probability they the dealership will be dissolved is 0.01478

Learn more : https://brainly.com/question/12474772

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