Answer:
The standard deviation of that data set is 3.8
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 55
95% of the data fall between 47.4 and 62.6. This means that 47.4 is 2 standard deviations below the mean and 62.6 is two standard deviations above the mean.
Using one of these points.
55 + 2sd = 62.6
2sd = 7.6
sd = 7.6/2
sd = 3.8
The standard deviation of that data set is 3.8
