a) Z = ( × - μ ) ÷ σ Where μ mean of population σ standard deviation Z is the abscissa to give the area or probability we are looking for associated to the value 10 ounces ( × )

So: Z = ( 10 - 9 ) ÷ 1.2 ⇒ Z = 1/1.2 ⇒ Z = 0.83 it has to be below this value

From Z tables we get P [ Z ≤ 0.82 ] = 0.7910 0r 79.10 %

b) Following the same procedure: We look for

P [ Z > ( x - μ ) ÷ σ ] ⇒ Z = ( 12 -10 ) ÷ 1.2 = 2.5

From Z table we get the area under the curve from the left tail up to the point Z < 2.5 ( 2.5 not included) but we were asked for the area out of that previous so 1- 0.9930 = 0.007 is the area we are looking for

So P (b) = 0.007 or 7 %

Finally between the two points above mentioned ( 10 ≤ Z ≤ 12 ) we use the previous values (taking in consideration the limits, according to the problem statement )

Z ≤ 10 Z ⇒( 10-9 ) ÷ 1.2 Z = 0.7967

Z ≥ 12 Z ⇒ ( 12 - 9 ) ÷ 1.2 Z = 0.9952

The interval is between these two points

0.9952 - 0.7967 = 0.1985 ⇒ or 19.85 %

The attached help in the understanding of the solution

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3 years ago