The amounts a soft drink machine is designed to dispense for each drink are norm

Question

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.4 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected. Find the probability that the drink is less than 12.2 fluid ounces. Find the probability that the drink is between 11.9 and 12.2 fluid ounces. Find the probability that the drink is more than 13 fluid ounces. Can this be considered an unusual event? Explain your reasoning. The probability that the drink is less than 12.2 fluid ounces is ___. (Round to four decimal places as needed.)

Explanation / Answer

Mean = 12.4 fluid ounces

Standard deviation = 0.3 fluid ounces

a) P(X<12.2) = P(Z < (12.2 - mean)/standard deviation)

= P(Z < (12.2 - 12.4)/0.3)

= P(Z < -0.67)

= 0.2514

b) P(11.9 < X < 12.2)

= P(X<12.2) - P(X<11.9)

= 0.2514 - P(Z < (11.9 - 12.4)/0.3)

= 0.2514 - P(Z < -1.67)

= 0.2514 - 0.0475

= 0.2039

c) P(X>13) = 1 - P(X<13)

= 1 - P(Z < (13-12.4)/0.3)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

This event has less than 5% chance of occurance and hence it can be considered unusual

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