Question

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8617 g and a standard deviation of 0.0517 g. A sample of these candies came from a package containing 440 ​candies, and the package label stated that the net weight is 375.5 g.​ (If every package has 440 ​candies, the mean weight of the candies must exceed StartFraction 375.5 Over 440 EndFraction equals0.8535 g for the net contents to weigh at least 375.5 ​g.)

Answer 1

Solution :

mean = = 0.8617

standard deviation = = 0.0517

n = 440

=   = 0.8617

= / n = 0.0517 / 440 = 0.0025

P( > 0.8535) = 1 - P( < 0.8535)

= 1 - P[( - ) / < (0.8535 - 0.8617) /0.0025 ]

= 1 - P(z < -3.28)

Using z table,    

= 1 - 0.0005

= 0.9995