Question

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule. (a) What proportion of the students scored at least 19 points on this test, rounded to five decimal places? (b) What is the 42 percentile of the distribution of test scores, rounded to three decimal places?

Answer 1

Answer:-

Given That:-

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 19 points on this test, rounded to five decimal places?

Given,

Here  

= P(Z < -1.5)

= 0.0668

(b) What is the 42 percentile of the distribution of test scores, rounded to three decimal places?

We want to compute 42th percentile

we use formula

P(Z < z) = 0.42

P(Z < -0.202) = 0.42

Therefore

X = 22 + (-0.202)*2

X = 21.596

42th percentile = 21.596

Thank you for your supporting. Please upvote my answer...

z = -0.202