Respuesta :
Answer:
The number of passes in a class of 180 is 75.
Step-by-step explanation:
The problem does not state, so I will suppose the passing grade is 70.
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 question:
[tex]\mu = 67.4, \sigma = 12[/tex]
Proportion of students who passed:
This is 1 subtracted by the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 67.4}{12}[/tex]
[tex]Z = 0.22[/tex]
[tex]Z = 0.22[/tex] has a pvalue of 0.5871.
1 - 0.5871 = 0.4129
Out of 180:
0.4129*180 = 74.32
Rounding up
The number of passes in a class of 180 is 75.
