Question

The amounts a soft drink machine is designed to dispense for each drink are normally? distributed, with a mean of 11.9 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected. ?

(a) Find the probability that the drink is less than 11.8 fluid ounces. ?

(b) Find the probability that the drink is between 11.5 and 11.8 fluid ounces. ?

(c) Find the probability that the drink is more than 12.4 fluid ounces. Can this be considered an unusual? event? explain your reasoning

Answer 1

a)

Z = ( - Mean ) SD

P( Z < 11.8) = ( 11.8 - 11.9) 0.2

P( Z < 11.8) = -0.5

From the normal distribution table, the probability is calculated as 0.3085

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b) P ( 11.5 < Z < 11.8)

P ( 11.5 < Z) = ( 11.5 - 11.9) 0.2

P ( 11.5 < Z) = 0.0228

P( Z < 11.8) = (11.8 - 11.9) 0.2

P( Z < 11.8) = 0.3085

P ( 11.5 < Z < 11.8) = 0.3085 - 0.0228

P ( 11.5 < Z < 11.8) = 0.2857

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c) P( Z 12.4 ) = ( 12.4 - 11.9) 0.2  

P( Z 12.4 ) = .9938

P(Z > 12.4) = 1 - 0.9938

P(Z > 12.4) = 0.0062

This can be considered as an unsual event because the probability that the drink is more than 12.4 fluid ounces has the lowest chance of occurence.