Question

A shipment of cereal boxes is delivered to a supermarket. The manager is told that the weights of the cereal boxes are normally distributed, with a mean of 165 g and a standard deviation of 5 g.

A. Find the probability that the random sample of 200 boxes has a mean weight of between 164.9 and 165.1.

B. Do I need to state that the distribution of the weights of the cereal boxes is normal in order to do part A? Answer in a single sentence.

Answer 1

Solution :

Given that ,

mean = = 165

standard deviation = = 5

n = 200

= 165

=  / n= 5 / 200=0.3536

P(164.9 <    < 165.1) = P[(164.9 -165) /0.3536 < ( - ) / < (165.1 -165) / 0.3536)]

= P( -0.28< Z <0.28 )

= P(Z <0.28 ) - P(Z <-0.28 )

Using z table

=0.6103 -0.3897

=0.2206

probability= 0.2206