Question

Please help, I’m unsure how to do standard deviation so I’m very confused!

Answer 1

a. With an average/mean of 7 dreams, one standard deviation away from the mean corresponds to the interval [7 - 1.7, 7 + 1.7] = [5.3, 8.7]. So children within one standard deviation of the mean experience somewhere between 5 and 9 dreams. Two standard deviations from the mean refers to the interval [7 - 2 * 1.7, 7 + 2 * 1.7] = [3.6, 10.4]. So children in this range have between 3.6 and 10.4 dreams.

b. We already know that the interval [5.3, 8.7] is one standard deviation from the mean. If we assume the number of dreams is normally distributed with mean 7 and standard deviation 1.7, then we can apply the empirical rule (a.k.a. 68-95-99.7), which says that for any normal distribution, roughly 68% of the distribution falls within one standard deviation of the mean. So we can expect roughly 68% of the 4800 children to have between 5.3 and 8.7 dreams, or about 3264 students.