Respuesta :
Using the normal distribution, it is found that there is a 0.5899 = 58.99% probability that on any given day it will take between 34 and 44 minutes to complete the task.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It 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, which is the percentile of X.
In this problem:
- Mean of 40 minutes, hence [tex]\mu = 40[/tex].
- Standard deviation of 6 minutes, hence [tex]\sigma = 6[/tex].
The probability that on any given day it will take between 34 and 44 minutes to complete the task is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 34, hence:
X = 44:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44 - 40}{6}[/tex]
[tex]Z = 0.67[/tex]
[tex]Z = 0.67[/tex] has a p-value of 0.7486
X = 34:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{34 - 40}{6}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587
0.7486 - 0.1587 = 0.5899.
0.5899 = 58.99% probability that on any given day it will take between 34 and 44 minutes to complete the task.
A similar problem is given at https://brainly.com/question/24663213
