A cola-dispensing machine is set to dispense 10 ounces of cola per cup, with a s

Question

A cola-dispensing machine is set to dispense 10 ounces of cola per cup, with a standard deviation of 0.5 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 31, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.

a. At what value should the control limit be set? (Round z values to two decimal places. (Round your answers to 2 decimal places.)

Value should be in between ___ and ___.

b. If the population mean shifts to 9.5, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

Probability is ___.          

c. If the population mean shifts to 10.4, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

Probability is ___.             

Explanation / Answer

for here std error =std deviation/(n)1/2 =0.0898

for 5% below and above; z=1.64485

a) hence confidence interval =mean +/- z*std deviation =9.85 ; 10.15

b)P(X>10.15)+P(X<9.85)=P(Z>(10.15-9.5)/0.0898)+P(Z<(9.85-9.5)/0.0898)

=P(Z>7.238)+P(Z<3.897)=0+1 =1

c)

P(X>10.15)+P(X<9.85)=P(Z>(10.15-10.4)/0.0898)+P(Z<(9.85-10.4)/0.0898)

=P(Z>-2.7839)+P(Z<-6.12)=0.9973

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