SOLUTION: Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 169 cm and a standard deviation of 6 cm. Using the empirical​ rule, what is the approx

Algebra ->  Probability-and-statistics -> SOLUTION: Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 169 cm and a standard deviation of 6 cm. Using the empirical​ rule, what is the approx      Log On


   

Question 1066528: Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 169 cm and a standard deviation of 6 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values;
a. 151 cm and 187 cm
b. 157 cm and 181 cm
can you please show steps so I can understand how to solve this?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
mean is 169 and sd is 6
x is the value given
z=(151-169)/6 and that is -18/6 or -3
z=(187-169)/6=18/6=3
so you want z to be between -3 and 3. That is by the empirical rule 99.7%
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For 157 and 181
z=(157-169)/6=-2, because -12/6=-2
z=(181-169)/6=2
That is z between -2 and 2, which by the empirical rule is 95%