normal distribution 18

As of Feb 2018, the median pay rate for a Production Worker is $12.40/hr. Assume a 40 hour work week, that the pay rates are normally distributed, and the mean pay rate is $12.40/hr with a standard deviation of $1.56/hr.

1. In a large database, we can assume range = about 6 standard deviations. If the range of data were $7.72/hr to $17.08/hr, estimate the standard deviation?

2. What is the probability a worker earned between $400 and $500 in a week?

3. How much did a production worker have to earn in a week to be in the top 10% of wage earners?

4. For a randomly selected production worker, what is the probability the worker earned less than $260 per week?