SOLUTION: Let X be the variable that represents the height of the individuals of a given population. Suppose that X has approximately normal distribution, with mean 170 cm and variance of 10

Question 1105420: Let X be the variable that represents the height of the individuals of a given population. Suppose that X has approximately normal distribution, with mean 170 cm and variance of 100 cm^2.
a) What is the probability that an individual of this population has height less than 175 cm?
b) Find the points a and b, symmetrical about the mean, such that P (a
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Less than 175 is z<(175-170)/10, (x-mean)/sd, and sd is the sqrt (var)
z<+(5/10) or +(1/2)
Probability is 0.6915.
The probability of being symmetric to the mean and having a probability of 0.50 requires the z-value of 0.2500 probability, which is +/-0.675
z=0.675=(x-170)/10
6.75=x-170
x=176.75
(163.25, 176.75)
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