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 between 62 and 106, to the nearest thousandth?
To find the probability that a randomly chosen person's IQ score will be between 62 and 106, we need to calculate the z-scores for these two IQ scores.
For an IQ score of 62:
Z = (62 - 100) / 15
Z = -38 / 15
Z = -2.53
For an IQ score of 106:
Z = (106 - 100) / 15
Z = 6 / 15
Z = 0.4
Next, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find these probabilities.
Using a calculator or software, we find that the probability of a z-score being between -2.53 and 0.4 is approximately 0.672.
Therefore, the probability that a randomly chosen person's IQ score will be between 62 and 106 is approximately 0.672 or 67.2%.