Question

4. The weights of adult German Shepherds are normally distributed. 1, 036 randomly selected German Shepherds were weighed for the survey

(a) Approximately how many dogs will fall within one standard deviation of the mean?

(b) Approximately how many dogs will be more than three standard deviations from the mean weight?

Answer 1

As the data follows the normal distribution we can use emperical rules

(a) Approximately how many dogs will fall within one standard deviation of the mean?

We know that within one standard deviation of mean 68% data lies ( 68.26% to be precise )

Hence 68%

(b) Approximately how many dogs will be more than three standard deviations from the mean weight?

We know that within three standard deviation of mean 99.75% data lies  

Hence outside the interval = 100 - 99.75 = 0.25%