Respuesta :
Answer:
There is a 9.34% probability that this project will be completed less than 21 days and 12 hours.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 25, \sigma = 2.645[/tex]
What is the probability that this project will be completed less than 21 days and 12 hours?
21 days and 12 hours is 21.5 days.
This probability is the pvalue of Z when X = 21.5. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 25}{2.645}[/tex]
[tex]Z = -1.32[/tex]
[tex]Z = -1.32[/tex] has a pvalue of 0.0934.
There is a 9.34% probability that this project will be completed less than 21 days and 12 hours.
