Final answer:
To find the probability of a randomly selected adult having an IQ score less than 100 when the mean IQ is 120 and the standard deviation is 20, you calculate a z-score of -1 and then refer to a z-table, revealing a probability of 15.87%.
Step-by-step explanation:
To calculate the probability that a randomly selected adult has an IQ score less than 100 with a mean IQ of 120 and a standard deviation of 20, we use the standard normal distribution. First, we convert the IQ score to a z-score, which is the number of standard deviations the score is from the mean. The formula to calculate this is:
Z = (X - μ) / σ
Where X is the score (100), μ is the mean (120), and σ is the standard deviation (20).
So the z-score for an IQ of 100 is:
Z = (100 - 120) / 20 = -1
Next, we consult the z-table or use a calculator with normal distribution functions to find the probability associated with a z-score of -1. This value represents the probability that a selected person has an IQ score less than 100. The probability associated with a z-score of -1 is approximately 0.1587. Therefore, there is a 15.87% chance that a randomly selected adult will have an IQ score less than 100.