Question

A company pays its employees an average wage of $3.25/hour with a standard deviation of $0.60. If the wages are approximately normally distributed, determine: [5x4=20pts] …graph a normal curve in all 4 parts.

a. The probability that randomly chosen worker has the hourly wage less than $3.

b. the proportion of the workers getting wages between $2.75 and $3.69 an hour

c. the minimum wage of the highest 8% of all workers.

Answer 1

Solution :

Given that ,

mean = = 3.25

standard deviation = = 0.60

a) P(x < 3 ) = P[(x - ) / < (3 -3.25 / 0.60]

= P(z <-0.42 )

= 0.3372

probability = 0.3372

b)

P( 2.75 < x < 3.69 ) = P[(2.75 -3.25)/0.60 ) < (x - ) /  < (3.69 -3.25) /0.60 ) ]

= P( -0.83< z < 0.73 )

= P(z <0.73 ) - P(z < -0.83 )

Using standard normal table

= 0.7673 - 0.2033 = 0.564

Probability =0.5640

c)

P(Z > z ) = 0.08

1- P(z < z) =0.08

P(z < z) = 1-0.08 = 0.92

z =1.405

Using z-score formula,

x = z * +

x =1.405*0.60 + 3.25

x = 2.45

Minimum wage = 4.09