Question

Use the z-score table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.

The weights of all the boxes of corn flakes filled by a machine are normally distributed, with a mean weight of 13.5 ounces and a standard deviation of 0.4 ounce. What percent of the boxes will have the following weights? (Round your answers to one decimal place.)

(a) weigh less than 13 ounces
%

(b) weigh between 12.5 ounces and 14.5 ounces
%

Answer 1

solution

given that

(A)P(X<13 ) = P[(X- ) / < (13 -13.5) / 0.4]

= P(z <-1.25 )

Using z table

= 0.1056

answer=10.6%

(B) P(12.5< x <14.5 ) = P[(12.5-13.5) /0.4 < (x - ) / < (14.5-13.5) /0.4 )]

= P( -2.5< Z <2.5 )

= P(Z < 2.5) - P(Z <-2.5 )

Using z table   

= 0.9938-0.0062

=0.9876

answer=98.8%