You must put the percent symbol on percentages. Round decimals to 3 decimal plac

Question

You must put the percent symbol on percentages.

Round decimals to 3 decimal places before changing decimals to percents.

Ex.   0.3456345 = 0.346 = 34.6%

2. The weights of boxes of Brand Z cereal were found to be normally distributed with a mean of 17.0 ounces and a standard deviation of 0.4 ounces.

a) What percentage of the boxes will weigh more than 17.5 ounces?

b) What percentage of the boxes will weigh between 16.5 and 17.5 ounces?

c) What percentage of the boxes will weigh less than 16.8 ounces?

d) What percentage of the boxes will weigh less than 16.5 ounces?

e) If a store has 500 boxes of cereal, how manyof boxes will weigh less than 16.5 ounces?

Explanation / Answer

Mean=17

StdD=0.4

a) Z=(17.5-17)/0.4=1.25

Pr(X>17.5)=1-Pr(X<=17.5)=1-Pr(Z)=1-Pr(1.25)=1-0.89435=0.10565=0.106=10.6%

b) Z1=(16.5-17)/0.4= -1.25

Z2=(17.5-17)/0.4=1.25

Pr(16.5<X<17.5)=Pr(Z2)-Pr(Z1)=0.89435-0.10565=0.789=78.9%

c) Z=(16.8-17)/0.4=-0.5

Pr(X<16.8)=Pr(Z)=Pr(-0.5)=0.309=30.9%

d) Z=(16.5-17)/0.4=-1.25

Pr(X<16.5)=Pr(Z)=Pr(-1.25)=0.10565=10.6%

e) Number of boxes that will weigh less than 16.5 ounces = Total no. of boxes * Probability=500*0.10565=52.82

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