A statistician is reviewing a dataset of the ages of a random sample of 500 people. The ages are normally distributed, with a mean of 35 and a standard deviation of 10. The statistician is interested in the proportion of the sample that falls between the ages of 25 and 45. Use the standard normal distribution to answer this question. Additionally, the statistician is looking for the roots of the quadratic equation (x^2 - 5x + 6 = 0). Factor the equation and find the roots.

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Step:1 ：Step 1: Convert the ages 25 and 45 into z-scores using the formula (z = frac{x - mu}{sigma}). The z-scores for 25 and 45 are (-1) and (1) respectively. The proportion of values between these z-scores can be found using the standard normal distribution table. It is approximately 0.6827 or 68.27%.Step:2 ：Step 2: To find the roots of the quadratic equation, factor the equation. (x^2 - 5x + 6 = 0) can be written as ((x - 2)(x - 3) = 0).Step:3 ：Step 3: Set each factor equal to zero and solve for x. The roots of the equation are (x = 2) and (x = 3).

Answer

Step: 1 ：Step 1: Convert the ages 25 and 45 into z-scores using the formula (z = frac{x - mu}{sigma}). The z-scores for 25 and 45 are (-1) and (1) respectively. The proportion of values between these z-scores can be found using the standard normal distribution table. It is approximately 0.6827 or 68.27%.Step: 2 ：Step 2: To find the roots of the quadratic equation, factor the equation. (x^2 - 5x + 6 = 0) can be written as ((x - 2)(x - 3) = 0).Step: 3 ：Step 3: Set each factor equal to zero and solve for x. The roots of the equation are (x = 2) and (x = 3).

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