the scores on a test are normally distributed with a mean of 130 and a standard deviation of 26. what is the…

the scores on a test are normally distributed with a mean of 130 and a standard deviation of 26. what is the score that is 3 standard deviations below the mean? a score of □ is 3 standard deviations below the mean.

the scores on a test are normally distributed with a mean of 130 and a standard deviation of 26. what is the score that is 3 standard deviations below the mean? a score of □ is 3 standard deviations below the mean.

Answer

Explanation:

Step1: Recall the formula for z - score

The formula for z - score is (z=\frac{x-\mu}{\sigma}), where (x) is the raw score, (\mu) is the mean, and (\sigma) is the standard deviation. We are given that (z=- 3) (since it is 3 standard deviations below the mean), (\mu = 130), and (\sigma=26).

Step2: Substitute the values into the formula and solve for (x)

Substitute (z=-3), (\mu = 130), and (\sigma = 26) into (z=\frac{x-\mu}{\sigma}). We get (-3=\frac{x - 130}{26}). Multiply both sides by 26: (-3\times26=x - 130). (-78=x - 130). Add 130 to both sides: (x=130-78).

Answer:

(52)