For each question.

• What is the random variable? X (discrete), X (continuous)
• What tool are you utilizing?
  • X ~ binomial
  • X ~ Normal
  • Xbar ~ Normal
  • Pbar ~ Normal
• What conditions need to be met to use this tool (if any), are they met?

Question 1

The amount of widgets an employee is able to make in a day is assumed normal with a mean of 200 and a standard deviation of 15 widgets.

Over the course of a week you have the following daily production amounts:

{ 250, 186, 203, 178, 233 }

Management pays out a weekly bonus to those in the top 5% of average weekly production.

• Would you qualify for this bonus?
• What's the probability of a worker having an average weekly production more than you?

Question 2

it is known that 70% of all workers exceed their daily targets. If management were to take a random sample of 50 workers, what would be the probability that between 50% and 60% of those selected exceeded their daily targets.