For a normal distribution with mean of 35 and standard deviation of 3, compute the following:A. What percent of all observations will fall between 32 and 38 ? % B. What percent of all observations will fall between 32 and 35 ? % C. What percent of all observations will fall above 35 ? % D. What percent of all observations will fall below 38 ? %
Accepted Solution
A:
A. The empirical rule tells you that 68% of observations fall within one standard deviation of the mean for a normal distribution. [32, 38] = 35 ±3, so your interval is within one standard deviation of the mean. 68% of observations will fall between 32 and 38
B. The distribution is symmetrical about the mean, so half of the observations in part A will be below the mean. 34% of observations will fall between 32 and 35
C. The distribution is symmetrical about the mean, so half the observations fall above the mean. 50% of observations will fall above 35
D. The distribution is symmetrical about the mean, so half the observations will fall below the mean, 35. As in part B, 34% will fall between the mean and one standard deviation above the mean, 38. The sum of these percentages is 84%. 84% of observations will fall below 38