SOLUTION: Can somebody help me solve these problems? a. If we are focused on 68% of the normal distribution, what percentage of the distribution is left in the upper tail only? On the

Question 1061989: Can somebody help me solve these problems?
a. If we are focused on 68% of the normal distribution, what percentage of the distribution is left in the upper tail only?
On the average, members at a local fitness center work out for 90 minutes with a standard deviation of 15 minutes.�The distribution is normal.

b. What percentage of the fitness club members work out for 45 minutes or less?
c. What percentage of the fitness club members work out for 2 hours and 15 minutes or more?
d. 68% of the fitness club members work out between which two time intervals?
e. How many minutes did 99.7% of the fitness club members work out for?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. 32% are in both tails so 16% will be in the top tail (slightly less but no big deal).
b. 45 minutes or fewer is 3 sd to the left. That is 0.3%. You get that by subtracting the mean from the value they gave you and dividing by the sd. That gives you the number of sd s. They are minus (to the left) or plus (to the right). The curve is symmetrical.
c. 135 minutes (2h15m) is 45 minutes the other direction and the same answer, 0.3%
d. 68% were within 1 sd, so that is between 75 and 105 minutes.
e.99.7% were within 3 sd s of the mean so between 45 and 135 minutes.
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