SOLUTION: 8. The mean of a normal probability distribution is 60; the standard deviation is 5.
a. About what percent of the observations lie between 55 and 65?
b. About what percent of t
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Question 648023: 8. The mean of a normal probability distribution is 60; the standard deviation is 5.
a. About what percent of the observations lie between 55 and 65?
b. About what percent of the observations lie between 50 and 70?
c. About what percent of the observations lie between 45 and 75?
PLEASE HELP!!!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
http://www.mathsisfun.com/data/standard-normal-distribution.html
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