Question

If continuous random variable X is normally distributed with µ = 256.43 and σ = 27.11, what is P(225.76 ≤ X ≤ 300.35)?

95.44%
5.26%
81.82%
87.08%

Answer 1

81.82%

Explanation:

First we need to convert the X score to Z score using the formula;

Z = X-µ/σ

If X = 225.76

Z = 225.76-256.43/27.11

Z = -30.67/27.11

Z = -1.1313

Similarly if X = 300.35

Z = 300.35-256.43/27.11

Z = 43.92/27.11

Z = 1.6201

Hence the required z score is P(-1.1313 ≤ Z ≤ 1.6201)

Checking the normal distribution table;

P( Z ≤ 1.6201) = 0.9474 = 94.74%

P(Z ≤ -1.1313) = 0.1292 = 12.92%

P(-1.1313 ≤ Z ≤ 1.6201) = 94.74 - 12.92

P(-1.1313 ≤ Z ≤ 1.6201) = 81.82%