What is the mean height for this population?

Question

in a cetain population of normally distributed hieghts with standard deviation of 3'', it is known that 30% of the population is shorter than 67 inches. What is the mean height for this population?

Answer 1

The Z score for a population is:

 

Z = (sample - mean)/(standard deviation)

• sample = 67 inches
• standard deviation = 3 inches

 

Z = (67 - mean)/3

mean = 67 - 3Z

 

Using a Z score table, look up a value of 0.3 and read the corresponding Z score.  The answer is Z = -0.52.

 

Mean = 67 - 3(-0.52) = 68.56 inches