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
%
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%
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