Answer:
The proportion of individuals score at most 74 points on this test is 70%.
Step-by-step explanation:
The complete question is:
Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 8. What proportion of individuals score at most 74 points on this test? Round your answer to at least four decimal places.
Solution:
Let X represent the scores on a reading ability test.
It is provided that [tex]X\sim N(70,8^{2})[/tex].
Compute the probability that an individuals score is at most 74 points on this test as follows:
[tex]P(X\leq 74)=P(\frac{X-\mu}{\sigma}\leq \frac{74-70}{8})[/tex]
[tex]=P(Z<0.50)\\=0.69146\\\approx 0.70[/tex]
Thus, the proportion of individuals score at most 74 points on this test is 70%.
