Question

Assume that adults have 1Q scores that are normally distributed with a mean of 99 and a standard deviation 152 . Find the first quartile Q1, which is the 1Q score separating the bottom 25% from the top 75%. (Hint. Draw a graph.)

The first quartile is (Type an integer or decimal rounded to one decimal place as needed.)

Answer 1

To find the first quartile Q1, calculate the z-score corresponding to the 25th percentile and solve for x using the z-score formula.

Step-by-step explanation:

To find the first quartile Q1, which separates the bottom 25% from the top 75% of scores, we need to calculate the z-score corresponding to this percentile using the standard normal distribution.

The z-score formula is z = (x - μ) / σ, where x is the given score, μ is the mean, and σ is the standard deviation.

For Q1, we have the percentile as 25%, so we need to find the z-score that corresponds to this percentile, which is approximately -0.6745. Solving the z-score formula for x, we get x = -0.6745 * σ + μ.

Substituting the values of μ = 99 and σ = 152 into the formula, we find Q1 = -0.6745 * 152 + 99, which gives Q1 ≈ 7.36.

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