Question

The weekly wages of employees of Volta gold are normally distributed about a mean of $1250 with a variance of $120. Find the probability of an employee having a weekly wage lying: i. Between $1320 and $970. ii. Under $1400. iii. Over $1290

Answer 1

0.7102

0.8943

0.3696

Explanation:

Given :

Mean , μ = 1250

Standard y, σ = 120

A.) Between $1320 and $970

P(Z < (x - μ) /σ) - P(Z < (x - μ) / σ))

P(Z < (1320 - 1250) /120) - P(Z < (970 - 1250) / 120))

P(Z < 0.5833) - P(Z < - 2.333)

Using the standard normal table or Z probability calculator :

0.7200 - 0.0098 = 0.7102

=0.71023

B. Under 1400

x = 1400

P(Z < (1400 - 1250) /120

P(Z < 1.25) = 0.8943

C.)

Over 1290

P(Z > Z)

P(Z > (1290 - 1250) /120 = 0.3333

P(Z > z) = 1 - P(Z < 0.3333) =

P(Z < 0.3333) = 0.6304

P(Z > 0.3333) = 1 - 0.6304 = 0.3696