If the expected time of completion of a project is 60 weeks with a standard deviation of 5 weeks, the probability of completing the project in 50 weeks and 65 weeks respectively will be A. 2.3% and 84.1% B. 97.7% and 84.1% C. 97.7 % and 15.9% D. 15.9% and 97.7%

2.3% and 84.1%
97.7% and 84.1%
97.7 % and 15.9%
15.9% and 97.7%

The correct answer is $\boxed{\text{C}}$.

The probability of completing a project in a given amount of time is given by the following formula:

$$P(T \leq t) = \Phi \left(\frac{t – \mu}{\sigma} \right)$$

where $\mu$ is the expected time of completion, $\sigma$ is the standard deviation, and $\Phi$ is the cumulative distribution function of the standard normal distribution.

In this case, $\mu = 60$ and $\sigma = 5$. So, the probability of completing the project in 50 weeks is:

$$P(T \leq 50) = \Phi \left(\frac{50 – 60}{5} \right) = \Phi(-2) \approx 0.023$$

The probability of completing the project in 65 weeks is:

$$P(T \leq 65) = \Phi \left(\frac{65 – 60}{5} \right) = \Phi(1) \approx 0.841$$

Therefore, the probability of completing the project in 50 weeks and 65 weeks respectively is $\boxed{\text{C}}$, 2.3% and 84.1%.

Option A is incorrect because the probability of completing the project in 50 weeks is less than 2.3%. Option B is incorrect because the probability of completing the project in 65 weeks is greater than 84.1%. Option D is incorrect because the probability of completing the project in 50 weeks is greater than the probability of completing the project in 65 weeks.

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