Answer:
The probability that a randomly selected person scores above 125 on the IQ test is 0.0062.
Step-by-step explanation:
We are given that the the scores on an IQ test are approximately normally distributed with a mean of 100 and a standard deviation of 10.
<em>Let X = scores on an IQ test</em>
The z-score probability distribution is given by ;
Z = ~ N(0,1)
where, = mean score = 100
= standard deviation = 10
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, the probability that a randomly selected person scores above 125 on the IQ test is given by = P(X > 125)
P(X > 125) = P( > ) = P(Z > 2.50) = 1 - P(Z 2.50)
= 1 - 0.9938 = 0.0062 <em>The above probability is calculated using z table by looking at value of x = 2.50 in the z table which have an area of 0.99379.</em>
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Therefore, probability that a randomly selected person scores above 125 on the IQ test is 0.0062.