Answer to Question #288217 in Statistics and Probability for isara

Question

1.   Assume that the exam result of Data Science class fits a normal distribution. Furthermore, the mean exam result  is 82, and the standard deviation is 17.2. What is the percentage of students scoring 90 or more in the exam?

Answer 1

Solution:

$\mu=82, \sigma=17.2 \\ X\sim N(\mu,\sigma) \\ P(X\ge 90)=1-P(X \le 90) \\=1-P(z\le \dfrac{90-82}{17.2}) \\=1-P(0.47) \\=1-0.68082 \\=0.31918$