Beer bottles are filled so that they contain an average of 360 ml of beer in eac

Question

Beer bottles are filled so that they contain an average of 360 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. Use Table 1. a. What is the probability that a randomly selected bottle will have less than 356 ml of beer? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability b. What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 356 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability c. What is the probability that a randomly selected 12-pack of beer will have a mean amount less than 356 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

Mean is 360 and s is 7. z can be calculated as (x-mean)/s

a) P(x<356)=P(z<(356-360)/7)=P(z<-0.57) or 1-P(z<0.57). from normal distribution table we get 1-0.7157=0.2843

b) here standard error, SE becomes s/sqrt(N) =7/sqrt(6)=2.86

thus P(x<356)=P(z<(356-360)/2.86)=P(z<-1.4) or 1-P(z<1.4). thus normal distribution is 1-0.9192 =0.0808

c) here standard error, SE becomes s/sqrt(N) =7/sqrt(12)=2.02

thus  P(x<356)=P(z<(356-360)/2.02)=P(z<-1.98) or 1-P(z<1.98). thus normal distribution is 1-0.9761 =0.0239

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