The number of steps taken in a day amongst a population is normally distributed with an average of 5000 steps a day with a standard deviation of 1600 steps. (model steps as a continuous random variable).

• What is the probability that an individual, selected at random, takes between 5500 and 6500 steps in a day?
• What would be the minimum number of steps needed to be taken in a day to be part of the top decile of the population?

Suppose that there is a 20% chance that an individual hits their step goal on a given day. You take a sample of 1500 individuals.

• What is the probability that more than 330 in your sample have hit their step goal on a given day?
• Compute the first quartile of this data set.