Question

: A chocolate producer releases chocolate in 10 gram packages. It is known that the weights of chocolate packages fit the normal distribution with a standard deviation of 0.5 g.

a) What is the probability that a randomly selected chocolate package weighs less than 11 grams?
b) How many packs should be over 11 grams in 1000 packs of randomly selected chocolate?

Answer 1

Solution :

Given that ,

mean = = 10

standard deviation = = 0.5

P(x < 11 )

= P[(x - ) / < ( 11 - 10) / 0.5 ]

= P(z < 2 )

Using z table,

= 0.9772

Probability = 0.9772

b.

P(x > 11 ) = 1 - P( x < 11 )

= 1- P[(x - ) / < ( 11 - 10) / 0.5 ]

= 1- P(z < 2 )

Using z table,

= 1 - 0.9772

= 0.0228 * 1000

= 22.8

Answer = 23