$2$

$3.$

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 $9$ ounces.

a$.$ The process standard deviation is $0\mathrm{.}15,$ and the process control is set at plus or minus $1$ standard deviation. Units with weights less than $8\mathrm{.}85$ or greater than $9\mathrm{.}15$ ounces will be classified as defects. What is the probability of a defect $($to $4$ decimals$)?$

$4.$

$5$

$6.$

$7.$

In a production run of $1,000$ parts, how many defects would be found $($to the nearest whole number$)?$

$8.$

$9.$

b$.$ Through process design improvements, the process standard deviation can be reduced to $0\mathrm{.}05.$ Assume the process control remains the same, with weights less than $8\mathrm{.}85$ or greater than $9\mathrm{.}15$ ounces being classified as defects. What is the probability of a defect $($to $4$ decimals$)?$

$10.$

$11.$

In a production run of $1,000$ parts, how many defects would be found $($to the nearest whole number$)?$

$12.$

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?