Question

Across the hospitality sector, it is found that the average wage paid for casual staff on weekends is $21.50 per hour with a standard deviation of $1.50 per hour. If casual staff hourly wages are assumed normally distributed, what is the value of the hourly wage if only 5% of all casual workers earn more than this wage?

Answer 1

Solution:- The value of the hourly wage if only 5% of all casual workers earn more than this wage is $23.97.

Mean = 21.50, S.D = 1.50

p-value for the top 5% = 1 - 0.05 = 0.95

z-score for the p-value = 1.645

By applying normal distribution:-

x - 21.50 = 2.4675

x = 2.4675 + 21.50

x = 23.9675