IQ scores are normally distributed with a mean u = 100 and a standard deviation o =15. Based on distribution, determine

% of IQ scores between 100 and 120 =

mean = 100

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion between score and mean related to the Z score. Multiply by 100.

the mean IQ in a certain sorority is 120 with SD of 5. What is the probability of selecting a random student whose IQ between 130 and 135?

To determine the percentage of IQ scores between 100 and 120, we need to calculate the z-scores for both values and then look up the corresponding probabilities using a standard normal distribution table or calculator.

First, we calculate the z-score for a score of 100 using the formula:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.
In this case, x = 100, μ = 100, and σ = 15.
z = (100 - 100) / 15 = 0

Next, we calculate the z-score for a score of 120:
z = (x - μ) / σ
Using the same formula but with x = 120, μ = 100, and σ = 15:
z = (120 - 100) / 15 = 1.33

Now, we can look up the probabilities associated with these z-scores using a standard normal distribution table or calculator.

The probability corresponding to a z-score of 0 is 0.5000, which represents the middle point in a standard normal distribution.

The probability corresponding to a z-score of 1.33 is 0.9088, which represents the area under the normal curve to the left of the z-score.

To find the percentage between these two scores, we subtract the probability for a z-score of 0 from the probability for a z-score of 1.33:
P(100 < x < 120) = P(z < 1.33) - P(z < 0) = 0.9088 - 0.5000 = 0.4088

Finally, we convert this probability to a percentage by multiplying by 100:
% of IQ scores between 100 and 120 = 0.4088 * 100 = 40.88%

Therefore, approximately 40.88% of IQ scores fall between 100 and 120.

To determine the percentage of IQ scores between 100 and 120, we need to calculate the area under the normal distribution curve between these two values.

Step 1: Convert the values to z-scores
To do this, we use the formula: z = (x - u) / o

For the lower bound, x = 100, u = 100, and o = 15:
z1 = (100 - 100) / 15 = 0

For the upper bound, x = 120, u = 100, and o = 15:
z2 = (120 - 100) / 15 = 1.33 (rounded to two decimal places)

Step 2: Find the area under the curve
We can use a z-table or a calculator with a normal distribution function to find the area under the curve between these two z-scores.

Using a standard normal distribution table, we can find the area to the left of z1 (0) and z2 (1.33).
For z1 = 0, the area to the left is 0.5000.
For z2 = 1.33, the area to the left is 0.9088.

To find the area between z1 and z2, we subtract the area to the left of z1 from the area to the left of z2:
Area = 0.9088 - 0.5000 = 0.4088

Step 3: Convert the area to a percentage
To convert the area to a percentage, we multiply it by 100.
Percentage = 0.4088 * 100 ≈ 40.88%

Therefore, approximately 40.88% of IQ scores are between 100 and 120.