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 11.8 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected. (a) Find the probability that the drink is less than 11.7 fluid ounces. (b) Find the probability that the drink is between 11.4 and 11.7 fluid ounces. (c) Find the probability that the drink is more than 12.1 flu d ounces. Can this be considered an unusual event? Explain your reasoning. (a) The probability that the drink is less than 11.7 fluid ounces is (Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

mean (x) =11.8 sd (s)= 0.2

a) p( x< 11.7)=P(z < 11.7-11.8/0.2)

=p(z < -0.5)

= 0.308538

=0.3085

b)p( 11.4<Z<11.7)= P(Z<11.7)-p(Z<11.4)

= 0.308538 -P(Z< 11.4-11.8/0.2)

=0.308538-0.02275

=0.285778

=0.2858

C)P(Z>12.1) =1-P(z<12.1)

=1-p( z< 12.1-11.8/0.2)

=1-P(z<1.5)

=1-0.933193

=0.066807

=0.0668

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