Answer :
Final answer:
To find the probability that a randomly selected adult has an IQ greater than 128.7, we can use the normal distribution and the z-score formula. The approximate probability is 0.0314.
Explanation:
To find the probability that a randomly selected adult has an IQ greater than 128.7, we can use the normal distribution and the z-score formula. The z-score formula is given by z = (x - mean) / standard deviation. We can calculate the z-score and then use the standard normal distribution table (or a calculator) to find the corresponding probability.
In this case, we have a mean of 97.4 and a standard deviation of 16.8. Substituting these values into the z-score formula, we get z = (128.7 - 97.4) / 16.8 = 1.86. Using the standard normal distribution table or a calculator, we can find the area to the right of z = 1.86, which represents the probability that a randomly selected adult has an IQ greater than 128.7. The approximate probability is 0.0314.
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