Question

5. BONUS QUESTION (10 pts) The packaging process in a breakfast cereal startup company has been adjusted so that an average net weight of 13.0 ounces of cereal is placed in each package. The standard deviation of the actual net weight is 0.1 ounces, and the variation follows a normal distribution. Determine the probability that a randomly chosen package will contain between 12.9 and 13.2 ounces of cereal. Include an illustration of the graph with your answer.

Answer 1

Solution :

Given that ,

mean = = 13

standard deviation = = 0.1

P(12.9< x <13.2 ) = P[(12.9-13) /0.1 < (x - ) / < (13.2-13) /0.1 )]

= P(-1 < Z <2 )

= P(Z <2 ) - P(Z < -1)

Using z table   

= 0.9772 - 0.1587

probability=  0.8185