"Scores on the Wechsler IQ test approximate a normal curve with a mean of 100 and a standard deviation of 15.
b. What percentage of IQ scores are below 74?"
I've been working at this for a while now, but when I solve for the z-score, I keep getting a negative number.
z=(74-100)/15 == -1.73
I remember talking about this in class, but can't find it in my notes or textbook, so I would appreciate any help I can get. Thank you in advance!
http://en.wikipedia.org/wiki/Intelligence_quotient
My confusion isn't with the idea of IQ scores, I'm having trouble calculating the z-score when the number given is less than the mean. My answer doesn't make logical sense like it would if the x number was higher than the mean. If you could walk me through that I would appreciate it.
Oops, never mind. I understand what I was doing wrong. Thank you :)
To find the percentage of IQ scores below 74, you need to calculate the cumulative probability associated with the z-score of -1.73. The cumulative probability represents the area under the normal distribution curve up to that specific z-score.
When you get a negative z-score, it means you are calculating the probability in the left tail (the area to the left of the z-score). In this case, you want to find the area to the left of -1.73.
Since the standard normal distribution is symmetrical, you can use a z-table or a calculator to find the cumulative probability associated with -1.73.
Here's how you can use a z-table:
1. Look for the absolute value of the z-score in the body of the table. In this case, we will look for the value 1.73.
2. The value in the body of the table represents the area to the left of the z-score. Since we have a negative z-score, the probability will be less than 0.5.
3. Find the column corresponding to the tenths digit of the z-score. In this case, we use column 0.07.
4. Find the row corresponding to the hundredths digit of the z-score. In this case, we use row 0.03.
5. The intersection of the row and column will give you the cumulative probability. For -1.73, the value is 0.0418.
6. Since you want the percentage, multiply this probability by 100: 0.0418 * 100 = 4.18%.
Therefore, approximately 4.18% of IQ scores are below 74.