Respuesta :
Answer:
37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade
Step-by-step explanation:
Problems of normally distributed samples are 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 = 12.6, \sigma = 2.5[/tex]
What is the probability that randomly selected homework will require between 8 and 12 minutes to grade?
This is the pvalue of Z when X = 12 subtracted by the pvalue of Z when X = 8. So
X = 12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12 - 12.6}{2.5}[/tex]
[tex]Z = -0.24[/tex]
[tex]Z = -0.24[/tex] has a pvalue of 0.4052
X = 8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 12.6}{2.5}[/tex]
[tex]Z = -1.84[/tex]
[tex]Z = -1.84[/tex] has a pvalue of 0.0329
0.4052 - 0.0329 = 0.3723
37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade
