Answer to Question #178316 in Statistics and Probability for anis

Question

A teacher realizes that his students' marks on a statistic test are normally distributed with a mean of 62 and a standard deviation of 15. If the teacher wishes to assign minimum marks for grade B is referring to the top 30 per cent of the students' marks in the class, how many marks are required to get a minimum mark for grade B?

Answer 1

$μ=62 \\ σ=15$

Determine the z-score in the normal probability that corresponds with the probability of 1 - 0.3 = 0.70:

$z= 0.52 \\ z = \frac{x-μ}{σ} \\ x = μ + zσ \\ x = 62 + 0.52 \times 15 = 69.8 ≈70$

So, 70 marks are required to get a minimum mark for grade B