Question

Given that x is a normal variable with mean μ = 108 and standard deviation σ = 14, find the following probabilities. (Round your answers to four decimal places.) (a) P(x ≤ 120) (b) P(x ≥ 80) (c) P(108 ≤ x ≤ 117)

Answer 1

We are given the distribution here as:

a) The probability here is computed as:

P( X <= 120)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.1957 is the required probability here.

b) The probability here is computed as:

P( X >= 80)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.9772 is the required probability here.

c) The probability here is computed as:

P( 108 < X < 117)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.2398 is the required probability here.