Question

Scores on the Wechsler Adult Intelligence Scale (an IQ test) for the 20- to 34-year-old age group are approximately Normally distributed with mu = 110 and sigma = 25. MENSA is an elite organization that admits as members people who score in the top 2

1) 105
2) 110
3) 115
4) 120

Answer 1

The question involves applying principles of normal distribution to IQ test scores, particularly for determining membership eligibility for MENSA and probabilities of scoring within specific ranges on the Wechsler Adult Intelligence Scale.

Step-by-step explanation:

The question pertains to the calculation of probabilities involving IQ scores and their distribution, specifically related to the Wechsler Adult Intelligence Scale and membership criteria for MENSA. When addressing the questions regarding the probability of scores between given ranges, the normal distribution and its properties are utilized. Using the mean (\(\mu\)) and standard deviation (\(\sigma\)) along with z-scores, one can determine probabilities for a certain range of IQ scores. For MENSA membership, the top 2% cutoff can be ascertained by looking up the corresponding z-score that yields a cumulative probability of 0.98 (as 100% - 2% = 98% percentile).

To find the probabilities, one would typically utilize z-tables or statistical software to verify where scores fall within the distribution. The example probability question given discusses finding the likelihood that a sample mean falls within a certain IQ range given a population mean and standard deviation.