assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 20. find the probability that a randomly selected adult has an IQ less than 20.

http://www.iqcomparisonsite.com/IQBasics.aspx

Z = (score-mean)/SD

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

To solve this problem, we need to calculate the z-score first. The z-score represents the number of standard deviations a given value is from the mean. The formula to calculate the z-score is:

z = (x - μ) / σ

Where:
x = the value we want to find the probability for (in this case, 20)
μ = the mean (100)
σ = the standard deviation (20)

Substituting the given values into the formula:

z = (20 - 100) / 20
z = -80 / 20
z = -4

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -4. The probability of obtaining a z-score of -4 or less is approximately 0.0000317.

Therefore, the probability that a randomly selected adult has an IQ less than 20 is approximately 0.0000317 or 0.00317%.

To find the probability that a randomly selected adult has an IQ less than 20, we need to calculate the z-score and then use a standard normal distribution table or calculator.

Step 1: Calculate the z-score
The z-score formula is: z = (x - μ) / σ

Given:
Mean (μ) = 100
Standard Deviation (σ) = 20
IQ score (x) = 20

z = (20 - 100) / 20
z = -80 / 20
z = -4

Step 2: Find the probability using the z-score
Now that we have the z-score, we can find the probability using a standard normal distribution table or calculator.

Using a standard normal distribution table, find the value that corresponds to z = -4. In most tables, you'll find that it is close to zero.

Since the left tail area corresponds to the probability of an IQ score less than 20, the probability is very small.

Therefore, the probability that a randomly selected adult has an IQ score less than 20 is approximately 0 (or close to 0).

Note: In real-world contexts, it is highly unlikely to find an adult with an IQ score less than 20, given the mean and standard deviation provided.