Respuesta :
Answer:
A.0.4477
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 = 16.3, \sigma = 4.2[/tex]
What is the probability that a randomly selected exam will require between 14 and 19 minutes to grade?
This probability is the pvalue of Z when X = 19 subtracted by the pvalue of Z when X = 14. So
X = 19
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 16.3}{4.2}[/tex]
[tex]Z = 0.64[/tex]
[tex]Z = 0.64[/tex] has a pvalue of 0.7389.
X = 14
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14 - 16.3}{4.2}[/tex]
[tex]Z = -0.55[/tex]
[tex]Z = -0.55[/tex] has a pvalue of 0.2912
0.7389 - 0.2912 = 0.4477
So the correct answer is:
A.0.4477
