Respuesta :
Using the normal distribution, the project completion time with a 75% certainty is of 42 weeks.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
For this problem, the parameters are given as follows:
[tex]\mu = 40, \sigma = \sqrt{9} = 3[/tex]
The project completion time with a 75% certainty is the 75th percentile, which is X when Z = 0.675, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.675 = (X - 40)/3
X - 40 = 3 x 0.675
X = 42.
The project completion time with a 75% certainty is of 42 weeks.
More can be learned about the normal distribution at https://brainly.com/question/24537145
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