If a distribution has mean 50 and standard deviation 5, approximately what values lie within one standard deviation of the mean?

If a distribution has mean 50 and standard deviation 5, approximately what values lie within one standard deviation of the mean?

• A. 50 to 60
• B. 40 to 60
• C. 45 to 55
• D. 45 to 50

Answer: (C)

The key idea is that one standard deviation around the mean defines the interval from mean minus standard deviation to mean plus standard deviation. With a mean of 50 and a standard deviation of 5, that interval is 50 − 5 to 50 + 5, i.e., 45 to 55. So values within one standard deviation lie between 45 and 55. The other options don’t cover this full range: starting at 50 misses values below 50, extending to 60 goes too high on the upper end, and 45 to 50 only covers half the interval.

The key idea is that one standard deviation around the mean defines the interval from mean minus standard deviation to mean plus standard deviation. With a mean of 50 and a standard deviation of 5, that interval is 50 − 5 to 50 + 5, i.e., 45 to 55. So values within one standard deviation lie between 45 and 55. The other options don’t cover this full range: starting at 50 misses values below 50, extending to 60 goes too high on the upper end, and 45 to 50 only covers half the interval.