Question

Internet service providers (ISP) need to resolve customer problems as quickly as possible. The probability for a customer call regarding Internet service interruption is resolved within one hour is 70%. During one day, the company had 10 customer calls. (10 marks)

a) What is the probability that exactly four of the customers had their problems solved? (Round your answer to the nearest thousandth).

Answer 1

The probability that exactly four customers had their problems solved is 0.250.

Step-by-step explanation:

To find the probability that exactly four customers had their problems solved, we can use the binomial probability formula:

`P(X=k) = (nCk) * p^k * (1-p)^(n-k)`

where n is the number of trials, k is the number of successes, p is the probability of success, and (nCk) represents the number of combinations.

For this problem, n = 10, k = 4, and p = 0.70.

Plugging in these values into the formula, we get:

`P(X=4) = (10C4) * (0.70^4) * (1-0.70)^(10-4)`

= 0.250

Answer 2

Answer: 0.037

Step-by-step explanation:

The probability that exactly four of the customers had their problems solved will be 0.037.

Check attachment for further details. Note that 10!/6!4! = (10×9×8×7×6×5×4×3×2×1)/(6×5×4×3×2×1×4×3×2×1) = 210

Therefore,

= 210 × 0.7⁴ × 0.3^6

= 0.037