Answer:
0.726 is the probability that the project will be completed in 33 days or less.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 30 days
Variance = 25 days
Standard Deviation,
[tex]\sigma = \sqrt{\text{Variance}} = \sqrt{25} = 5[/tex]
We assume that the distribution of path length is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(completed in 33 days or less)
[tex]P( x \leq 33) = P( z \leq \displaystyle\frac{33 - 30}{5}) = P(z \leq 0.6)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x \leq 33) = 0.726 = 72.6\%[/tex]
0.726 is the probability that the project will be completed in 33 days or less.
