Question

# A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard...

A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 37, 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.

1. 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 .

2. If the population mean shifts to 7.6, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

 Probability

3. If the population mean shifts to 8.6, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

 Probability

1) here for top and bottom 5% critical value =1.64

hence Value should be in between =mean-/+z*std error=8-/+1.64*1/sqrt(37)=7.73 and 8.27

2)

 for normal distribution z score =(X-μ)/σx here mean=       μ= 7.6 std deviation   =σ= 1.000 sample size       =n= 37 std error=σx̅=σ/√n= 0.1644

probability that the change will not be detected:

 probability = P(7.73

3)

 probability = P(7.73

#### Earn Coins

Coins can be redeemed for fabulous gifts.