IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly chosen person's IQ score will be less than 65, to the nearest thousandth?
To find the probability that a randomly chosen person's IQ score will be less than 65, we need to find the z-score associated with 65 and then use a z-table to find the corresponding probability.
First, calculate the z-score:
z = (X - μ) / σ
z = (65 - 100) / 15
z = -2.33
Next, we look up the corresponding probability in a standard normal distribution table. The probability for a z-score of -2.33 is 0.0099.
Therefore, the probability that a randomly chosen person's IQ score will be less than 65 is approximately 0.0099 or 0.010 when rounded to the nearest thousandth.