SOLUTION: If the mean of a normal distribution is 70 and the standard deviation is 3, what is the z-value for 73? given that the heights are normally distributed with a mean of 70 inches an

Question 374488: If the mean of a normal distribution is 70 and the standard deviation is 3, what is the z-value for 73?
given that the heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches, what is the probability of a person chosen at random having a height between 67 and 73 inches?- here I have used the Bell shape with 99.7% within the 3 standard deviation range. I am thinking I am correct on this but not sure.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
Probability of being within 1 standard deviation ~68%... within two standard deviations from the mean ~95% and ... within 3 standard deviations ~99.7% Probability of a person chosen at random having a height between 67 and 73 inches is within '1 standard deviation of the mean' in this example (mean of 70 inches and a standard deviation of 3 inches)
Long hand:
P(height between 67 and 73 )
z = 73-70/3 = 1
z = 67-70/3 = -1
NORMSDIST(1) = .84135
NORMSDIST(-1)= .15866
P( height between 67 and 73) = .84135 - .15866 = .6827
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