Question

For a normal distribution, find the probability of being

(a) Within 1.49 standard deviations of the mean.

(b) Between μ−3σ μ − 3 σ and μ+1.5σ μ + 1.5 σ

(c) More than 1 standard deviations away from the mean

Use the Standard Normal Table in your textbook or Excel to obtain more accuracy.

Answer 1

Solution :

(a)

P(-1.49 < z < 1.49) = P(z < 1.19) - P(z < -1.49) = 0.9319 - 0.0681 = 0.8638

Probability = 0.8638

(b)

Using Empirical rule,

P( - 3< X < + 3) = 99.7%

Probability = 0.9970

P(-1.5 < z < 1.5) = P(z < 1.5) - P(z < 1.5) = 0.9332 - 0.0668 =0.8664

Probability = 0.8664

(c)

P(z < 1) = 0.8413

Probability = 0.8413