The probability that a randomly selected adult has an IQ less than 141.8 is

Answer 1

Hello Kelsy,

To find the probability that a randomly selected adult has an IQ less than 141.8, you typically need the mean (average) and standard deviation of the IQ scores in a normal distribution. Assuming a mean IQ of 100 and a standard deviation of 15 (which is a common approximation for IQ scores), you can use the standard normal distribution (Z-table) to calculate this probability.

First, calculate the Z-score for an IQ of 141.8 using the formula:

Z = (X - μ) / σ

Where:

- X is the value you want to find the probability for (141.8 in this case).

- μ (mu) is the mean IQ (100).

- σ (sigma) is the standard deviation (15).

Z = (141.8 - 100) / 15 ≈ 2.7867 (rounded to four decimal places)

Now, you can use the Z-table or a calculator to find the probability associated with this Z-score. The Z-table gives you the probability that a randomly selected value from a standard normal distribution is less than the Z-score. In this case, you want to find P(Z < 2.7867).

Using a Z-table or calculator, you can find the corresponding probability, which is approximately 0.9971. Therefore, the probability that a randomly selected adult has an IQ less than 141.8 is approximately 0.9971 or 99.71%.

Keep in mind that the specific values (mean and standard deviation) for IQ scores can vary, so it's important to use the appropriate parameters if they differ from the assumed values, I hope this helps out