Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 14 ounces.

a. The process standard deviation is 0.10 ounces, and the process control is set at plus or minus 2.25 standard deviations. Units with weights less than 13.775 or greater than 14.225 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)?

b. Through process design improvements, the process standard deviation can be reduced to 0.09 ounces. Assume the process control remains the same, with weights less than 13.775 or greater than 14.225 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?

In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

Let x be the number of bicycles owned by families in Canada, for which the probability distribution is as follows:

x 0 1 2 3 ________________________

p(x) .1 .3 .55 .05

a. What is the mean and standard deviation of x?

b. Show the sampling distribution of x̄ for random samples of N=2 measurements drawn from the probability distribution of x.

c.Determine whether or not x̄ is an unbiased estimator of μ

d. An ideal point estimator should be consistent. What does this mean?

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 14 ounces.

1. The process standard deviation is 0.1, and the process control is set at plus or minus 1.5 standard deviations. Units with weights less than 13.85 or greater than 14.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?
   
   
   In a production run of 1000 parts, how many defects would be found (to 0 decimals)?
   
   
2. Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same, with weights less than 13.85 or greater than 14.15 ounces being classified as defects. What is the probability of a defect (rounded to 4 decimals; getting the exact answer, although not necessary, will require Excel)?
   
   
   In a production run of 1000 parts, how many defects would be found (to 0 decimals)?
   

1. Suppose that two fair dice are rolled. Find the probability that the number on the first die is a 6 or the number on the second die is a 2.

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of ounces.

a. The process standard deviation is , and the process control is set at plus or minus standard deviation . Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of parts, how many defects would be found (round to the nearest whole number)?

b. Through process design improvements, the process standard deviation can be reduced to . Assume the process control remains the same, with weights less than or greater than ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of parts, how many defects would be found (to the nearest whole number)?

c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean?

If you know that the probability that a normal variable exceeds a certain number Q, is .10, you can be sure that the probability that this variable is less than -Q

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 11 ounces. a. The process standard deviation is .20 ounces, and the process control is set at plus or minus .75 standard deviations. Units with weights less than 10.85 or greater than 11.15 ounces will be classified as defects.

What is the probability of a defect (to 4 decimals)?

In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)?

b. Through process design improvements, the process standard deviation can be reduced to .07 ounces. Assume the process control remains the same, with weights less than 10.85 or greater than 11.15 ounces being classified as defects.

What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of ounces.

a. The process standard deviation is, and the process control is set at plus or minus standard deviation. Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of parts, how many defects would be found (round to the nearest whole number)?

b. Through process design improvements, the process standard deviation can be reduced to. Assume the process control remains the same, with weights less than or greater than ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of parts, how many defects would be found (to the nearest whole number)?

c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean?