Question

5. Assume that in a certain population IQ scores are normally distributed. It is observed that 80% of the population has an IQ grater than 100 and 4% of the mentioned population has an IQ less than 85. Find the mean and the standard deviation of the IQs of this population. What is the probability that a randomly selected person has an IQ score greater than 109?​

Answer 1

The mean and standard deviation of the IQ scores of a normal population can not be determined from the information given, i.e., the percentage of people with IQ scores greater than 100 and the percentage of people with IQ scores less than 85.

However, the probability that a randomly selected person has an IQ score greater than 109 can be calculated using the standard normal distribution. We need to first standardize the value of 109 by subtracting the mean and dividing by the standard deviation, and then look up the probability of a standard normal random variable being greater than this standardized value. As the mean and standard deviation are not given, this probability can not be calculated.