Respuesta :
Answer:
15.39% of the scores are less than 450
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 = 565, \sigma = 113[/tex]
What percentage of the scores are less than 450?
This is the pvalue of Z when X = 450. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{450 - 565}{113}[/tex]
[tex]Z = -1.02[/tex]
[tex]Z = -1.02[/tex] has a pvalue of 0.1539
15.39% of the scores are less than 450
