Assume that Y is normally distributed N(μ,σ2).Moving from the mean (μ)1.96 standard deviations to the left and 1.96 standard deviations to the right,then the area under the normal p.d.f.is
A)0.67
B)0.05
C)0.95
D)0.33

Question

Quizplus · Accepted Answer

Moving 1.96 standard deviations from the mean in each direction will give us the interval (μ-1.96σ,μ+1.96σ) which contains 95% of the area under the normal p.d.f. Since the normal distribution is symmetric, half of the area, or 0.475, is on each side of the mean. Therefore, the total area under the normal p.d.f. in this interval is 0.475+0.475=0.95.

Assume That Y Is Normally Distributed N(μ,σ2)