Question

The IQ scores for the students in a school is normally distributed. The mean is 110, and the standard deviation is 12. Find the following:

A student with an IQ of 120 would have a z-score of _________.
A student with an IQ of 90 would have a z-score of __________.
What IQ score would rank you in the 99th percentile?

A) A student with an IQ of 120 would have a z-score of 1.00. A student with an IQ of 90 would have a z-score of -1.67. An IQ score of 135 would rank you in the 99th percentile.
B) A student with an IQ of 120 would have a z-score of 1.00. A student with an IQ of 90 would have a z-score of -1.67. An IQ score of 108 would rank you in the 99th percentile.
C) A student with an IQ of 120 would have a z-score of 0.83. A student with an IQ of 90 would have a z-score of -1.00. An IQ score of 135 would rank you in the 99th percentile.
D) A student with an IQ of 120 would have a z-score of 0.83. A student with an IQ of 90 would have a z-score of -1.00. An IQ score of 108 would rank you in the 99th percentile.

Which of the following answer choices best describes Lincoln’s main purpose in making this speech?

A) Lincoln is inspiring his audience to face upcoming challenges by recounting historical events and comparing them to his present time.
B) Lincoln is warning his audience that continuing the present course of action will almost certainly lead to war.
C) Lincoln reflects on the principles of the historical document and how he intends to stand by them.
D) Lincoln presents evidence that the historical document guarantees peace in the new nation.

Question: Point K on the number line shows Kelvin's score after the first round of a quiz. In round 2, he lost 9 points. Which expression shows how many total points he has at the end of round 2?

A) 3 + (-6) = -9, because -9 is 6 units to the left of 3
B) 3 + 6 = -9, because -9 is 6 units to the left of 3
C) 3 + (-9) = -6, because -6 is 9 units to the left of 3
D) 3 + 9 = -6, because -6 is 9 units to the left of 3

Answer 1

To find the z-score of a given IQ score, subtract the mean from the score and divide by the standard deviation. To find the IQ score that would rank you in the 99th percentile, use the z-score to determine the corresponding IQ score.

Step-by-step explanation:

To find the z-score for a given IQ score, we use the formula:
z = (x - mean) / standard deviation

For a student with an IQ score of 120:
z = (120 - 110) / 12 = 1.00

For a student with an IQ score of 90:
z = (90 - 110) / 12 = -1.67

To find the IQ score that would rank you in the 99th percentile, we look up the z-score from a standard normal distribution table and find the corresponding IQ score. In this case, the z-score corresponding to the 99th percentile is approximately 2.33. Using the formula:
x = mean + (z * standard deviation)

x = 110 + (2.33 * 12) ≈ 136.96

So, the answer is A) A student with an IQ of 120 would have a z-score of 1.00. A student with an IQ of 90 would have a z-score of -1.67. An IQ score of 135 would rank you in the 99th percentile.