What is probability that a randomly selected adult has an IQ less than 115 ? Har

Question

What is probability that a randomly selected adult has an IQ less than 115 ?

Harsh Patel& 414/18 6:35 PM Homework: Normal Probability Distributions Sa Score: 0 of 1 pt 10 of 19 (7 complete) Hw Score: 32%, 8 of 25 A 6.2.13 E Question Help Assume that adults have I scores that are normally distributed with a mean of ? 100 and a standard deviation ?-15 Find the probability that a randomly selected adult has an IQ less than 115. Click to view page 1 of the table, Click to view page 2 of the table The probability that a randomly selected adult has an IQ less than 115 is (Type an integer or decimal rounded to four decimal places as needed.) tho nnswer hox and then click Check Answer

Explanation / Answer

P(x ? 115) = P(z ? (115 - 100)/15) = P(z ? 1) = 0.8413 = 84.13 % (from z table)

Alternatively,

The total area covered by one standard deviation is from IQs of 85 to 115. Since the standard deviation is 15, one standard deviation covers 15 points above and below the average.

With a normal distribution, we know that 68% of the scores will be covered by one standard deviation. Half of this 68% is above the average, while the other half is below the average. So, if 68% of the scores are from 85 to 115, the upper half of that (the scores from 100 to 115 ) is 34% of the scores.

So, if an IQ score of 0 to 100 represents 50% of the population (as 100 is mean) and an IQ score of 100 to 115 represents 34% of the population...then an IQ score of 115 or lower represents 50+34=84% of the population.

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