Question

The average weight of a box of cereal is 25.2 ounces with a standard deviation of 0.18 ounces. Quality control wants to make certain that the 10% heaviest boxes of cereal are not sent to the store to sell. What would be the cutoff weight for these cereal boxes?

Answer 1

Given that,

mean = = 25.2

standard deviation = =0.18

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.9

= P(Z < 1.28) = 0.9  

z = 1.28 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.28 * 0.18+25.2

x= 25.43