ľ Bob takes an online IQ test and finds that his IQ according to the test is 134. Assuming that the mean IQ is 100, the standard deviation is 15, and the distribution of IQ scores is normal, what proportion of the population would score higher than Bob? Lower than Bob?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the Z score.

The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.4 years. The standard deviation of the distribution is 2.6 years.


For a random sample of 57 men, what is the likelihood that the age at which they were married for the first time is less than 24.9 years?

To find the proportion of the population that would score higher or lower than Bob, we need to use the standard score, also known as the z-score. The z-score measures the number of standard deviations an individual's IQ score is above or below the mean.

To calculate the z-score, we use the formula:

z = (X - μ) / σ,

where X is the IQ score, μ is the mean, and σ is the standard deviation.

Let's calculate the z-score for Bob's IQ score:

z = (134 - 100) / 15
z = 34 / 15
z ≈ 2.27 (rounded to two decimal places)

Now, we can use the z-score to find the proportion of the population that would score higher or lower than Bob.

1. To find the proportion of the population that would score higher than Bob, we need to find the area under the normal distribution curve to the right of the z-score. We can consult a standard normal distribution table or use a statistical calculator.

Using a standard normal distribution table, a z-score of 2.27 corresponds to a proportion of approximately 0.988.

Therefore, about 98.8% of the population would score lower than Bob.

2. To find the proportion of the population that would score lower than Bob, we need to find the area under the normal distribution curve to the left of the z-score. Using the complement rule, we subtract the proportion found in the previous step from 1.

1 - 0.988 = 0.012 (rounded to three decimal places)

Therefore, approximately 1.2% of the population would score higher than Bob.

So, about 98.8% of the population would score lower than Bob, and approximately 1.2% would score higher than Bob.