Question

Suppose you got a score of 17 on a quiz. For which of the following conditions would your score indicate the best performance in relation to the rest of the class? (A) µ = 17 and σ = 2.4 (B) µ = 17 and σ = 2.1 (C) µ = 15 and σ = 2.4 (D) µ = 15 and σ = 2.1

Answer 1

For First and Second condition your score indicate the best performance in relation to the rest of the class.

Explanation:

We are given the following conditions :

(A) µ = 17 and σ = 2.4

(B) µ = 17 and σ = 2.1

(C) µ = 15 and σ = 2.4

(D) µ = 15 and σ = 2.1

Also, Suppose you got a score of 17 on a quiz.

And we have to find that which of the following conditions would your score indicate the best performance in relation to the rest of the class.

For finding in which of the following conditions would the score indicate the best performance in relation to the rest of the class, we will find the z score for each of the conditions because the higher the z score, it indicates the best performance.

The z-score probability distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = mean

`\sigma` = standard deviation

X = score on a quiz = 17

• The z-score of First condition is calculated as;

Since we are given that you got a score of 17 on a quiz and µ = 17 and σ = 2.4.

So, z-score =
`(17-17)/(2.4)` = 0

• The z-score of Second condition is calculated as;

Since we are given that you got a score of 17 on a quiz and µ = 17 and σ = 2.1.

So, z-score =
`(17-17)/(2.1)` = 0

• The z-score of Third condition is calculated as;

Since we are given that you got a score of 17 on a quiz and µ = 15 and σ = 2.4.

So, z-score =
`(15-17)/(2.4)` = -0.83

• The z-score of Fourth condition is calculated as;

Since we are given that you got a score of 17 on a quiz and µ = 15 and σ = 2.1.

So, z-score =
`(15-17)/(2.1)` = -0.95

AS we can clearly see that the z score of First and Second condition are equally likely higher as compared to third and Fourth condition so it can be stated that for First and Second condition your score indicate the best performance in relation to the rest of the class.