The actual volumes of soda in quart-sized bottles can be described by a Normal model with a mean of 32.3 fluid ounces and a standard deviation of 1.2 fluid ounces. What percentage of bottles can we expect to have a volume of less than 32 fluid ounces?

Question

Halle Hensley

Mathematics

14 January, 02:46

The actual volumes of soda in quart-sized bottles can be described by a Normal model with a mean of 32.3 fluid ounces and a standard deviation of 1.2 fluid ounces. What percentage of bottles can we expect to have a volume of less than 32 fluid ounces?

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Answers (1)

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Journey Conway · Answer 1

Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%

Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a = 32.3 oz

b=1.2 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S, a and b into the equation

Y=32-32.3/1.2

Y=-0.25

Probability of bottles that have a volume less than 32 oz is

P (S<32) = P (Y<-025) = 0.40129

Percentage of bottles that have volume less than 32 oz will be

0.40127*100%=40.13%