The average score of 100 students taking a statistics final was 70,with a standard deviation of 7. Assuming a normal distribution,what is the probability that a student scored 90 or higher?
A)0.4979
B)0.0021
C)0.9979
D)2.86

Question

Quizplus · Accepted Answer

To find the probability of a student scoring 90 or higher, we calculate the z-score for 90 using the formula z = (X - μ) / σ, where X is the score (90), μ is the mean (70), and σ is the standard deviation (7). This gives us a z-score of (90-70)/7 = 20/7 ≈ 2.86. Looking up this z-score in a standard normal distribution table or using a calculator, we find the probability of a z-score being above 2.86 is approximately 0.0021, indicating a very low probability of a student scoring 90 or higher.

The Average Score of 100 Students Taking a Statistics Final