the mean of a normally distributed set of data is 56, and the standard deviation is 5. in which interval do approximately 95.4% of all cases lie?

Question

the answers are either 46-56, 51-61, 46-66, 56-71

 

Answer 1

The answer should be 46 - 66

Area between the mean and the lower limit = 0.954/2 = 0.477

Area to the left of the lower limit = 0.5 - 0.477 = 0.023

the z-score of the lower limit when P<0.023 = - 2

Area to the left of the upper limit = 0.5 + 0.477 = 0.977

the z-score of the upper limit when P<0.977 = 2

The lower limit = 56 - 2*5 = 46

The upper limit = 56 + 2*5 = 66

The interval = 46 to 66