Question: A company's cereal boxes advertise that each box contains 9.65 ounces of cereal

A company's cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the probability distribution of Y= amount of cereal in a randomly selected box can be modeled by a normal distribution with mean µ=9.71 ounces and standard deviation s=0.03 ounce.

a. Sketch the normal density curve. Label the mean and the points that are 1,2 , and 3 standard deviations from the mean.

b. What is the probability that a randomly selected box will be less than the advertised weight?

c. About 68% ?of these boxes have weights between what two values?

DRAFT/STUDY TIPS

Let's break this down step by step.

a. Sketch the Normal Density Curve

For a normal distribution:

• The mean μ=9.71\mu = 9.71μ=9.71 ounces is the center of the curve.
• The standard deviation σ=0.03\sigma = 0.03σ=0.03 ounce determines the spread of the curve.