Question

The concentration of impurities in a semiconductor used in the production of microprocessors for computer is a normally distributed random variable with mean 127 parts per million (ppm) and standard deviation 22 parts per million. A semiconductor is acceptable only if its concentration of impurities is below 150 parts per million. What is the proportion of the semiconductors that are acceptable for use? (The area under the standard normal curve for the value of Z=1.05 is 0.3531)

Answer 1

Answer:

vmmmmmmmmmmmmmmmmmmmmmmmmmmm

jkkmmmmmmmmmmm

Answer 2

The acceptance value (150 ppm) is higher than the mean - which it had better be, if the supplier expects most of his materials to be accepted.

Explanation:

• In case were the impurities are < 127 ppm or the lower half of the distribution, all the materials will pass.
• That lower half of the distribution is 50% of the materials, will always pass.
• Now what about those materials on the upper half of the distribution - with impurities > 127 ppm? Only the fraction between 127 and 150 will pass. How many standard deviations is that from the mean?

• Z = 150-127/22

           =1.0455

• What fraction of the cumulative normal distribution is that?

        P(0 < Z ≤ 1.0455) = Φ(1.0455) − Φ(0) = 0.8508−0.5 = 0.3508.

• So what is the total fraction that will pass?This is the sum of the area where P (Z ≤ 0) = 0.5 and the area where P (0 < Z ≤ 1.0455) = 0.3508.

• So then, P (Z ≤ 0)+P (0 < Z ≤ 1.0455) = 0.5+0.3588 = 0.8588.
• This can also be done in one step: P (Z ≤ 1.0455) = Φ(1.0455) = 0.8588.

To Learn More...

1.The concentration of impurities in a semiconductor used in the production of microprocessors for computer is a normally distributed random variable with mean 127 parts per million (ppm) and standard deviation 22 parts per million. A semiconductor is acceptable only if its concentration of impurities is below 150 parts per million. What is the proportion of the semiconductors that are acceptable for use? (The area under the standard normal curve for the value of Z=1.05 is 0.3531)The concentration of impurities in a semiconductor used in the production of microprocessors for computer is a normally distributed random variable with mean 127 parts per million (ppm) and standard deviation 22 parts per million. A semiconductor is acceptable only if its concentration of impurities is below 150 parts per million. What is the proportion of the semiconductors that are acceptable for use? (The area under the standard normal curve for the value of Z=1.05 is 0.3531)​

https://brainly.in/question/16792534