Question

The mean weight of a box of cereal filled by a machine is 18.0 ounces, with a standard deviation of 0.5 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 17.5 ounces
%

(b) between 17.7 and 18.3 ounces
%

Answer 1

Solution :

Given that ,

a) P(x < 17.5)

= P[(x - ) / < (17.5 - 18.0) / 0.5]

= P(z < - 1)

Using z table,

= 0.1587

=15.87%

b) P( 17.7 < x < 18.3) = P[(17.7 - 18.0) / 0.5) < (x - ) /  < (18.3 - 18.0) / 0.5) ]

= P( - 0.6 < z < 0.6)

= P(z < 0.6) - P(z < - 0.6)

Using z table,

= 0.7257 - 0.2743

= 0.4514

= 45.14%