Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15.
Find the probability that a randomly selected adult has an IQ that is less than 115. Round to the nearest thousandth. Answer precisely. Do not use the Empirical rule to answer this question.
just find P(Z < 1)
since 115 is 1 std above the mean.
To find the probability that a randomly selected adult has an IQ less than 115, we need to calculate the area under the normal distribution curve up to that point.
First, we need to standardize the IQ score of 115 by using the z-score formula:
z = (x - μ) / σ
Where:
x = 115 (the IQ score you want to find the probability for)
μ = 100 (mean of the IQ scores)
σ = 15 (standard deviation of the IQ scores)
Plugging in the values, we get:
z = (115 - 100) / 15
z = 1
Now, we need to find the probability of a z-score less than 1. We can use a standard normal distribution table or a calculator to look up this probability.
Using a standard normal distribution table or a calculator, we find that the probability that a randomly selected adult has a z-score less than 1 is approximately 0.8413 (rounded to four decimal places).
Therefore, the probability that a randomly selected adult has an IQ less than 115 is approximately 0.8413 (rounded to four decimal places) or 84.13% (rounded to two decimal places).