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The probability that a single can will contain 11.6 ounces or less of soda is 0.2843
<h3>Probability that a can contains 11.6 ounces or less</h3>The given parameters are:
x = 11.6
Mean = 12
Standard deviation = 0.7
Calculate the z value using:
This gives
z = -0.57
The probability is then calculated as:
P(x ≤ 11.6) = P(z ≤ -0.57)
Using the z table of probabilities, we have:
P(x ≤ 11.6) = 0.2843
<h3>Probability that a pack contains 11.6 ounces or less</h3>In (a), the probability that a can contains 11.6 ounces or less is 0.2843
The probability that all cans in a pack contains 11.6 ounces or less is
P(6) = 0.2843^6
P(6) = 0.00053
<h3>Probability that a case contains 11.6 ounces or less</h3>In (a), the probability that a can contains 11.6 ounces or less is 0.2843
The probability that all cans in a case contains 11.6 ounces or less is
P(36) = 0.2843^36
P(36) ≈ 0
<h3>Draw three normal distributions</h3>See attachment for the normal distributions
<h3>The happening on the graph</h3>The summary of the graph is that, as the sample size increases the probability decreases
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