I'm kinda stuck on my math homework, does anyone know how to do it?
The results of a blood test at a medical lab are normally distributed with a mean of 60 and a standard deviation of 15. How low must a score be to lie in the lowest 5% of the results?
See:
http://www.jiskha.com/display.cgi?id=1307664839
To find the score that lies in the lowest 5% of the results, we need to use the concept of the standard normal distribution. Here's how to solve the problem step by step:
1. Standardize the score: To find the desired score, we first convert it into a standard score (also known as a z-score). The formula to standardize a score is: z = (x - μ) / σ, where x is the given score, μ is the mean, and σ is the standard deviation.
2. Find the z-score corresponding to the lowest 5%: Since we're interested in the lowest 5% of the results, we need to find the z-score that corresponds to the cumulative probability of 0.05. This can be done using a standard normal distribution table or a calculator/statistical software.
3. Solve for the score: Once we have the z-score, we can rearrange the standardization formula to solve for the score (x). The formula is: x = z * σ + μ.
Let's apply these steps to the problem:
1. Standardize the score: We have x = ?, μ = 60, and σ = 15. We'll represent the unknown score as x.
2. Find the z-score corresponding to the lowest 5%: Using a standard normal distribution table or calculator, the z-score that corresponds to a cumulative probability of 0.05 is approximately -1.645.
3. Solve for the score: Rearranging the standardization formula, we have x = z * σ + μ. Plugging in the values, we get x = -1.645 * 15 + 60.
Calculating this expression, we find x ≈ 34.83.
Therefore, the score must be approximately 34.83 or lower to lie in the lowest 5% of the results.