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Answer 1

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:

$z = \frac{x - \bar x}{\sigma}$

This gives

$z = \frac{11.6-12}{0.7}$

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:

brainly.com/question/11234923

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