Question

The mean weight of a box of cereal filled by a machine is 15.0 ounces, with a standard deviation of 0.4 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh the following amounts? (Round your answers to two decimal places.)

(a) less than 14.5 ounces %

(b) between 14.8 and 15.2 ounces %

Answer 1

Solution :

Given that,

mean = = 15.0

standard deviation = = 0.4  

P(X<14.5 ) = P[(X- ) / < (14.5-15.0) / 0.4]

= P(z <-1.25 )

Using z table

= 0.1056

answer=10.56%

(B)

P(14.8< x < 15.2) = P[(14.8-15.0) / 0.4< (x - ) / < (15.2-15.0) / 0.4 )]

= P(-0.5 < Z <0.5 )

= P(Z < 0.5) - P(Z < -0.5)

Using z table   

= 0.6915-0.3085

=0.3830

answer=38.30%