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Sagot :
The probability that a single can will contain 11.6 ounces or less of soda is 0.2843
Probability that a can contains 11.6 ounces or less
The given parameters are:
x = 11.6
Mean = 12
Standard deviation = 0.7
Calculate the z value using:
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
This gives
[tex]z = \frac{11.6-12}{0.7}[/tex]
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
Probability that a pack contains 11.6 ounces or less
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
Probability that a case contains 11.6 ounces or less
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
Draw three normal distributions
See attachment for the normal distributions
The happening on the graph
The summary of the graph is that, as the sample size increases the probability decreases
Read more about probability at:
https://brainly.com/question/11234923
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