a scientist calculated the mean and standard deviation of a data set to be $mu = 120$ and $sigma = 9$. she…

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?\n129\n147\n360\n369

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?\n129\n147\n360\n369

Answer

Explanation:

Step1: Recall the formula for value based on mean and std - dev

The formula for a value $x$ in terms of the mean $\mu$ and standard - deviation $\sigma$ is $x=\mu\pm k\sigma$, where $k$ is the number of standard deviations away from the mean. Here, $\mu = 120$, $\sigma=9$, and $k = 3$.

Step2: Calculate the missing data value

We have two cases: $x=\mu + k\sigma$ or $x=\mu - k\sigma$. If we consider the positive case (since the problem doesn't specify whether it's above or below the mean, and we'll assume above for simplicity as the options suggest positive deviation), $x=120+3\times9$. $x = 120+27$. $x=147$.

Answer:

B. 147