Final answer:
An average IQ score is around 100, though Jake's score may vary depending on the test used. When calculating probabilities for sample means, the normal distribution and z-scores are utilized. Scores within one standard deviation (85 to 115) are average, while scores of 130 or above indicate superior intelligence.
Step-by-step explanation:
If your friend Jake scored exactly average on an IQ test, his score would be around the mean IQ score, which is generally set at 100. However, when considering the probability that a sample of 20 randomly selected adults will have IQ scores between 85 and 125 points, it is important to use the principles of a normal distribution and standard deviations. A typical adult has an average IQ score of 105 with a standard deviation of 20. To find this probability, one would calculate the z-scores for 85 and 125, and then use the standard normal distribution to find the probability that the sample mean falls within that range.
Generally, any IQ score that falls within one standard deviation above or below the mean (85 to 115) is considered average. Thus, a score of 115 would be described as "one standard deviation above the mean." Anyone with an IQ score of 130 or above is considered to possess a superior level of intelligence or may be classified as "gifted." For the Mensa organization, members must have an IQ in the top 2% of the population.