160 athletes are distributed with a mean finishing time of 72.2 min and a standard deviation of 6.8 min What is # of athletes with finishing times between 58.6 and 72.2 min
In a standard bell curve, the mean finishing time is the middle of the curve. One standard deviation includes 68.2% of the values with 34.1% above and 34.1% below the mean. For two deviations it includes 95.4% of the values with 47.7% above and 47.7% below the mean.
In this problem 72.2 is the mean and 6.8 the standard deviation. One standard deviation below would include the range of values between 72.2 and 65.4(=72.2-6.8) the number of people in this range would be 34.1% of the total number of people. In this case its two standard deviations below which includes the range between 72.2 and 58.6(=72.2-2*6.8). This includes 47.7% of the total number of athletes who participated. So the answer would be 160*.477=76.32 or 76 since only counting whole people.