Respuesta :
Answer:
The numerical limits for a D grade is scores between 56 and 64.
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 = 70.9, \sigma = 9.89[/tex]
Find the numerical limits for a D grade.
Below the top 76%
Scores below X when Z has a pvalue of 1-0.76 = 0.24. So scores below X when Z = -0.705.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.705 = \frac{X - 70.9}{9.89}[/tex]
[tex]X - 70.9 = -0.705*9.89[/tex]
[tex]X = 64[/tex]
Above the bottom 6%
Above X when Z has a pvalue of 0.06. So above X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 70.9}{9.89}[/tex]
[tex]X - 70.9 = -1.555*9.89[/tex]
[tex]X = 56[/tex]
The numerical limits for a D grade is scores between 56 and 64.
