IQ test scores are normally distributed with a mean score of 100 and a standard deviation of 16.The probability that a randomly selected person has a IQ test score of over 140 is ?

To find the probability that a randomly selected person has an IQ test score of over 140, we need to calculate the z-score for an IQ score of 140 and then find the probability of a z-score greater than that value.

First, calculate the z-score:
z = (X - μ) / σ
z = (140 - 100) / 16
z = 2.5

Next, find the probability of a z-score greater than 2.5 using a standard normal distribution table or calculator. The probability of a z-score greater than 2.5 is approximately 0.0062.

Therefore, the probability that a randomly selected person has an IQ test score of over 140 is 0.0062, or 0.62%.

The probability that a randomly selected person has an IQ test score of over 140 is:

$$P(X > 140) = P\left ( \frac{X - 100}{16} > \frac{140 - 100}{16} \right )=P(Z > 2.5)$$

where Z is a standard normal random variable. Using a standard normal table or calculator, we find that:

$$P(Z > 2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062$$

Therefore, the probability that a randomly selected person has a IQ test score of over 140 is 0.0062 or 0.62%.