In a large statistics class, the correlation between midterm scores and final scores is found to be nearly 0.50, every term. The scatter diagrams are football-shaped. Predict the percentile rank on the final for a student whose percentile rank on the midterm is a) 5% b) 80% c) 50% d) unknown

A) 21%

B) 66%

C) 50%

D) 50%

Step-by-step explanation:

A) We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 5%.

Now, it means we are looking for the value of z on the 5th percentile.

Now from the Z-score percentile normal distribution table i have attached, the value of z on the 5th percentile is; Zx = -1.645

Now, using the regression method, we know that;

Zy = r(Zx)

Where Zy is the score at which the final percentile occurs.

And r = 0.5 from the question

Thus; Zy = 0.5 x -1.645

Zy = - 0.8225

Now looking at the table attached, there is no direct value of -0.8225,and so we pick the closest to it which is -0.8 and it falls on the 21st percentile.

Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 5% would be 21%.

B) We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 80%.

Following same pattern in A above;

From table, Zx = 0.842

And Zy = 0.5 x 0.842 = 0.421

The percentile for this value is approximately 66th percentile.

Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 80% would be 66%.

C)We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 50%.

Following same pattern in A above;

From table, Zx = 0

And Zy = 0.5 x 0 = 0

The percentile for this value is 50th percentile.

Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 50% would be 50%.

D) If the score is unknown, the best bet will be to use a middle percentile of 50%.

It thus follows the same procedure from c above and same answer of 50%.

18.8 cubic inches.

step-by-step explanation:

volume of a cone = πr²h

r = 1.5 inches

h = 8 inches

pi = 3.14

volume of our cone = × 3.14 × 1.5² × 8 = 18.84 square inches

or equals to 18.8 square inches rounded up to nearest tenth.

the answer is 0.000652422

but if you ment to ask what is 6131 divided by 4, it is 1532.75.

step-by-step explanation: