Question

What proportion of the students scored at least 23 points on this test, rounded to five decimal places

Answer 1

The proportion of students who scored at least 23 points on the test is thirty percent.

Step-by-step explanation:

In Solution 2.21, it is mentioned that thirty percent of students answered 16 or more questions correctly. So, the proportion of students who scored at least 23 points on the test can be estimated using this information. Since we know that 16 is less than 23, all the students who scored 16 or more points would have also scored at least 23. Therefore, the proportion of students who scored at least 23 points is also thirty percent.

Answer 2

This question is incomplete, the complete question is;

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.

What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

Answer:

proportion of the students that scored at least 23 points on this test is 0.30850

Step-by-step explanation:

Given the data in the question;

mean μ = 22

standard deviation σ = 2

since test closely followed a Normal Distribution

let

Z = x-μ / σ { standard normal random variable ]

Now, proportion of the students that scored at least 23 points on this test.

P( x ≥ 23 ) = P( (x-μ / σ) ≥ ( 23-22 / 2 )

= P( Z ≥ 1/2 )

= P( Z ≥ 0.5 )

= 1 - P( Z < 0.5 )

Now, from z table

{ we have P( Z < 0.5 ) = 0.6915 }

= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850

P( x ≥ 23 ) = 0.30850

Therefore, proportion of the students that scored at least 23 points on this test is 0.30850