SOLUTION: According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose

Question 1182611: According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches.
Suppose one Martian adult male is randomly chosen.
Let X = the height of the individual.
Round to 4 decimal places.
a. What is the distribution of X? X~N (64,2.3)

b. Find the probability that the person is between 63.5 and 65.4 inches tall?
c. The middle 30% of Martian heights lie between what 2 numbers?
Low ______ High _______

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. is X~N(64, 5.29) use variance as second part.
b. z is between (63.5-64)/2.3 and (65.4-64)/2.3 or between -0.217 and 0.609
this probability is 0.3146 (not rounding the z-values until the end give 0.3147.
c. this tis between z of -0.5244 and z of +0.5244. Find z from table or use 2ndVARS3(invnorm(0.30,0,1) and then change the sign for the second value, since the distribution is symmetric.
-0.5244=(x-64)/2.3
-1.21=x-64
x=62.8 inches and 65.2 inches

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