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 data - value in terms of mean and standard deviation

The formula for a data - 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 use the formula $x=\mu + k\sigma$ (assuming the positive direction; we could also consider the negative direction, but the options suggest we are looking at the positive side). Substitute the given values: $x=120+3\times9$. First, calculate $3\times9 = 27$. Then, $x=120 + 27=147$.

Answer:

147