6. Normal Distribution & Continuous Random Variables

Determine if each curve (in orange) is a valid probability density function (i.e. if the total area under the function = 1)

Determine if each curve (in orange) is a valid probability density function (i.e. if the total area under the function = 1)

Shade the area corresponding to the probability listed, then find the probability.

$P\left(2<X<4\right)$

Shade the area corresponding to the probability listed, then find the probability.

$P\left(X<7.5\right)$

A regional sales manager is forecasting sales for a new energy-efficient refrigerator. Based on market research she estimates that weekly sales will be uniformly distributed between 400 and 700 units. The company's operations team must decide how many units to stock per week to meet demand without overstocking. If they stock 550 units, find the probability of overstocking. If they want to have less than a 20% chance of overstocking, should they stock more or less than 550 units?