Question

a scientist calculated the mean and standard deviation of a data set to be $mu = 120$ and $sigma = 9$. she then found that she was missing one data value from the set. she knows that the missing data value was exactly 3 standard deviations away from the mean. what was the missing data value?
129
147
360
369

Explanation:

Step1: Recall the formula for data - value in terms of mean and standard deviation

The formula is $x=\mu + z\sigma$, where $\mu$ is the mean, $z$ is the number of standard - deviations from the mean, and $\sigma$ is the standard deviation.

Step2: Identify the given values

We are given that $\mu = 120$, $z = 3$, and $\sigma=9$.

Step3: Substitute the values into the formula

$x=120+3\times9$.

Step4: Calculate the result

$x = 120 + 27=147$.

Answer:

B. 147