Question

A company pays its employees an average wage of Rs 159 an hour with a standard deviation of Rs 15. If the wages per hour are approximately normally distributed, (i) what percentage of the workers receive wages between Rs 129 and Rs 189 in an hour? (ii) the highest 5% of the employee hourly wages is greater than what amount?

Answer 1

µ = 159, σ = 15

i) percentage of the workers that receive wages between 129 and 189 in an hour, P(129< X <189)=

= P( (129-159)/15 < (X-µ)/σ < (189-159)/15 )

= P(-2 < z < 2)

= P(z < 2) - P(z < -2)

Using excel function:

= NORM.S.DIST(2, 1) - NORM.S.DIST(-2, 1)

= 0.9545 = 95.45%

ii)

P(x > a) = 0.05

= 1 - P(x < a) = 0.05

= P(x < a) = 0.95

Z score at p = 0.95 using excel = NORM.S.INV(0.95) =1.6449

Value of X = µ + z*σ = 159 + (1.6449)*15 = 183.67

Highest 5% of the employee hourly wages is greater than Rs 183.67