b. What is the probability that the project will take less than 56 days to complete?

(Enter the probability to four decimal places in the format 0.xxxx . Do NOT convert to percentages.)

Question

b. What is the probability that the project will take less than 56 days to complete?

(Enter the probability to four decimal places in the format 0.xxxx . Do NOT convert to percentages.)

BlackTom AI · Accepted Answer

The question asks: b. What is the probability that the project will take less than 56 days to complete? (Enter the probability to four decimal places in the format 0.xxxx. Do NOT convert to percentages.)

First, note that there are no answer choices provided here, and no distribution or data about the project duration is included in the prompt. To determine a probability like P(X < 56) you need either:
- A statistical model for the project duration X (e.g., X ~ Normal(mu, sigma^2) or X ~ Lognormal with given parameters), or
- A dataset of observed project durations from which you can estimate the distribution (e.g., a sample of durations allowing empirical CDF calculation).

If the duration is modeled as a normal distribution, you would proceed as follows:
1) Identify mu (the mean duration) and sigma (the standard deviation) of X.
2) Compute the z-score: z = (56 - mu) / sigma.
3) Find the probability P(X < 56) = Phi(z), where Phi is the standard normal CDF.
4) Report the result to four decimal places in the format 0.xxxx.

If the duration is modeled as a lognormal distribution, you would:
1) Use parameters mu_log and sigma_log of the underlying normal distribution (log of X).
2) Compute z = (ln(56) - mu_log) / sigma_log.
3) Then P(X < 56) = Phi(z), and report as 0.xxxx.

If you only have a dataset of observed durations, you could:
1) Construct the empirical CDF from the data.
2) Look up the proportion of durations less than 56 days.
3) Report that proportion with four decimal places as 0.xxxx.

Without mu and sigma (or the actual data), it is not possible to calculate the numeric probability. If you can provide the distribution parameters (e.g., mean and standard deviation for a normal model, or the log-parameters for a lognormal model, or the raw durations), I can perform the calculation and give you the four-decimal result.

Additionally, ensure that when you compute or report the probability, you format it as a decimal between 0 and 1 with four digits after the decimal point, for example 0.1234, and not as a percentage.

COMM_V 191 201 202 203 204 2024W2 2024W2 - Assignment 5

b. What is the probability that the project will take less than 56 days to complete? (Enter the probability to four decimal places in the format 0.xxxx . Do NOT convert to percentages.)

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