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Math Help - Some normal Questions

  1. #1
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    Post Some normal Questions

    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?
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  2. #2
    Bar0n janvdl's Avatar
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    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
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