Question

Scores on a English test have average of 85 with standard deviation of 8. What is the probabilty of a student scoring less than 77 on the test? Write your answer as a percent.

Answer 1

Answer:47.725%

If the mean (μ) is 80, and the standard deviation (σ) is 5, then all scores between 80 and 90 would fall between 0 and 2 standard deviations above the mean.

Using the equation for Z score (Z = (X-μ)/σ) for each X value (80 and 90) then the Z scores are 0 and 2, respectively.  

Using a normal distribution table, it can be found that P(80 < z) = .5 (this is the probability that a random score would be greater than 80.  It makes sense that it is .5 or 50% because 80 is the mean.)

And the P(90 > z) = .97725.  (this is the probability that a random score would be less than 90.)

Answer 2

Answer:

10

Step-by-step explanation: