Question 648023
mean is 60.
standard deviation is 5.
calculate a z-score for each of the possibilities.
z-score = actual score minus mean divided by standard deviation.
for a:
z-score = (55-60)/5 and (65-60)/5 which results in:
z-score of -1 and 1.
this is 1 standard deviation above and below the mean which is approximately 68% of the distribution.
for b:
z-score = (50-60)/5 and (70-60)/5 which results in:
z-score of -2 and 2.
this is 2 standard deviations above and belowthe mean which is approximately 95% of the distribution.
for c:
z-score = (45-60)/5 and (75-60)/5 which results in:
z-score of -3 and 3.
this is 3 standard deviations above and below the mean which is approximately 99.7% of the distribution.
the actual figures are more detailed, but these are the generally recognized rounded figures that are normally used.
check out this link for further information regarding normal distribution and standard deviations from the mean.
<a href = "http://www.mathsisfun.com/data/standard-normal-distribution.html" target = "_blank">http://www.mathsisfun.com/data/standard-normal-distribution.html</a>