Some normal Questions

samira · #1 $Old$ 11-18-2008, 01:50 AM

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?

janvdl · #2 $Old$ 11-24-2008, 03:37 AM

Quote:

Originally Posted by samira $View Post$

Q.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?

a)
$P( X < 45)$

$= P \left( \frac{X - 60}{5} < \frac{45 - 60}{5} \right)$
$= P(Z < -3)$
$= 1 - P(Z < 3)$
$= 1 - 0,9987$
$= 0,0013$

b)
$P( X > 65)$

$= P(Z > 1)$
$= 1 - P(Z < 1)$
$= 1 - 0,8413$
$= 0,1587$

c)
$P( X < T) = 0,99$
$P \left( Z < \frac{T - 60}{5} \right) = 0,99$

Now look up which value will give you the closest approximation to 0,99 ; I found 4,9 to be sufficient.

$\frac{T-60}{5} = 4,9$

$1 - P(Z < 1)$
$T = 84,5 \ minutes$