MYP Extended Mathematics Interpreting Standard Deviation Questionbank

A distribution has $\mu = 100$ and $\sigma = 15$. An observation of $x = 145$ is ________ standard deviations above the mean.

A dataset representing the daily commute times of $25$ employees has a mean $\mu = 40\text{ minutes}$ and a standard deviation $\sigma = 10\text{ minutes}$. If additional employees are included in the survey, and all of them have a commute time of exactly , which of the following statements best describes the effect on the dataset?

A dataset has a mean $\mu = 50$ and a standard deviation $\sigma = 8$. A value $x$ is considered "within 1 standard deviation" if it falls in the interval ________.

If a height dataset is normally distributed with $\mu = 170\text{ cm}$ and $\sigma = 10\text{ cm}$, about 68% of the heights will be between ________.

When comparing the consistency of two manufacturing processes for producing engine parts, which statistic provides a direct measure of the "predictability" or "typical clustering" of the output size in the original units of measurement (e.g., millimeters)?