For the overall population, the IQ scores follow the normal distribution with mean equal to 100 and variance equal to 225. What is the best answer?

A. If you pick a person at random, the chance that his IQ falls
between 100 to 115 is more than the chance that his IQ falls
between 60-85.
B. If you pick a person at random, the chance that his IQ falls
between 100 to 115 is as compared to falling between 65 to 80
depends on the number of the outliers.
C. If you pick a person at random, the chance that his IQ falls
between 100 to 115 is not comparable to his IQ falling between
60-85.
D. If you pick a person at random, the chance that his IQ falls
between 100 to 115 is less than the chance that his IQ falls
between 65 to 80.

Standard deviation = square root of variance = 15

Z = (score-mean)/ SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to these Z scores.

D. If you pick a person at random, the chance that his IQ falls between 100 to 115 is less than the chance that his IQ falls between 65 to 80.

But let's face it, IQ scores are just numbers. It's not like they can measure how well you can juggle or tell a good joke. In that case, my IQ would be off the charts!

To answer this question, we need to compare the probabilities of certain ranges of IQ scores.

We know that IQ scores follow a normal distribution with a mean of 100 and a variance of 225.

Calculating the standard deviation (SD) from the variance, we find that SD = sqrt(225) = 15.

Now, we can convert the given IQ score ranges into z-scores, which represent the number of standard deviations an individual's IQ score falls from the mean.

For the range 100 to 115:
The z-score for 100 is (100 - 100) / 15 = 0.
The z-score for 115 is (115 - 100) / 15 = 1.

For the range 60 to 85:
The z-score for 60 is (60 - 100) / 15 = -2.67.
The z-score for 85 is (85 - 100) / 15 = -1.

Now, we can look up the probabilities associated with these z-scores in the standard normal distribution table or use a calculator.

The probability of an IQ falling between 100 and 115 is P(0 ≤ Z ≤ 1) ≈ 0.3413.

The probability of an IQ falling between 60 and 85 is P(-2.67 ≤ Z ≤ -1) ≈ 0.2022.

Comparing the probabilities, we can conclude that:

A. If you pick a person at random, the chance that his IQ falls between 100 to 115 is more than the chance that his IQ falls between 60-85.

Therefore, the correct answer is A.

To determine the best answer, we need to analyze the given information about the IQ scores.

The normal distribution is a symmetric bell-shaped curve where the mean (μ) represents the central tendency and the variance (σ²) represents the spread of the scores. In this case, the mean is 100 and the variance is 225.

Answer choice A states that the chance of a randomly picked person's IQ falling between 100 to 115 is more than the chance of it falling between 60 to 85. To determine the probability between the ranges, we need to calculate the z-scores.

The z-score is calculated by subtracting the mean from the given value and then dividing by the standard deviation (which is the square root of the variance). The formula is: z = (x - μ) / σ.

For the range 100 to 115:
z1 = (100 - 100) / sqrt(225) = 0
z2 = (115 - 100) / sqrt(225) = 1

To find the probability of an IQ falling between these values, we can refer to a standard normal distribution table or use statistical software to calculate this probability. The z-table gives us the area under the curve up to a specific z-score.

For the range 60 to 85:
z3 = (60 - 100) / sqrt(225) = -4
z4 = (85 - 100) / sqrt(225) = -1

Now we can compare the probabilities obtained from the z-table or a software.

Answer choice B does not provide relevant information about outliers, so it cannot be considered.

Answer choice C states that the chance of an IQ falling between 100 to 115 and 60 to 85 cannot be compared, but we can actually compare them using probability calculations.

Answer choice D states that the chance of an IQ falling between 100 to 115 is less than the chance of it falling between 65 to 80. Again, we need to compare the probabilities.

By calculating the z-scores and referring to a z-table or using statistical software, we can determine which range has a higher probability. The answer will be the option that correctly represents the comparison of the probabilities obtained.