Question

The amounts a soft drink machine is designed to dispense for each drink are normally? distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.

?(a) Find the probability that the drink is less than 12 fluid ounces.

?(b) Find the probability that the drink is between 11.9 and 12 fluid ounces.

?(c) Find the probability that the drink is more than 12.5 fluid ounces. Can this be considered an unusual? event? Explain your reasoning.

Answer 1

a) P(X < 12)

= P((X - )/ < (12 - )/)

= P(Z < (12 - 12.1)/0.3)

= P(Z < -0.33)

= 0.3707

b) P(11.9 < X < 12)

= P((11.9 - )/ < (X - )/ < (12 - )/)

= P((11.9 - 12.1)/0.3 < Z < (12 - 12.1)/0.3)

= P(-0.67 < Z < -0.33)

= P(Z < -0.33) - P(Z < -0.67)

= 0.3707 - 0.2514

= 0.1193

c) P(X > 12.5)

= P((X - )/ > (12.5 - )/)

= P(Z > (12.5 - 12.1)/0.3)

= P(Z > 1.33)

= 1 - P(Z < 1.33)

= 1 - 0.9082

= 0.0918

As the probability value is not less than 0.05, so this is not an unusual event.