Respuesta :
Answer:
38.3% of the people taking the test score between 400 and 500
Step-by-step explanation:
When the distribution is normal, we use 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 question, we have that:
[tex]\mu = 450, \sigma = 100[/tex]
What percentage of the people taking the test score between 400 and 500
We have to find the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 400. So
X = 500
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 450}{100}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915
X = 400
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{400 - 450}{100}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.3085
0.6915 - 0.3085 = 0.383
38.3% of the people taking the test score between 400 and 500
