plz tell in these qestion how to solve.. the method

Q1 Assume that in the detection of a digital signal the background noise follows a normal distribution

with a mean of 0 volt and standard deviation of 0.45 volt. The system assumes a digital

1 has been transmitted when the voltage exceeds 0.9.

a) What is the probability of detecting a digital 1 when none was sent?

b) Determine symmetric bounds about 0 that include 99% of all noise readings

c) Suppose a digital 1 is represented as a shift in the mean of the noise distribution to 1.8

volts. What is the probability that a digital 1 is not detected?

Q2. The diameter of a shaft in an optical storage drive is normally distributed with mean 0.2508

inch and standard deviation 0.0005 inch. The specifications on the shaft are 0.2500 +/- 0.0015

inch. What proportion of shafts conforms to specifications?

If the process is centered so that the process mean is equal to the target value of 0.2500,what is the % of yield ?

3. The line width of for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer.

(a) What is the probability that a line width is greater than

0.62 micrometer?

(b) What is the probability that a line width is between 0.47

and 0.63 micrometer?

(c) The line width of 90% of samples is below what value?

4. The time it takes a cell to divide (called mitosis) is normally distributed with an average time of one hour and a

standard deviation of 5 minutes.

(a) What is the probability that a cell divides in less than

45 minutes?

(b) What is the probability that it takes a cell more than

65 minutes to divide?

(c) What is the time that it takes approximately 99% of all

cells to complete mitosis?