statistics

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the life of electric bulbs has a normal distribution with a mean of 35 months and a standard deviation of 4 months. What should the warranty period be if the company that manufactures these bulbs does not want to replace more than 2% of the bulbs?

  • statistics -

    Z = (score-mean)/SD

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.02) and its Z score. Insert the value in the above equation and solve for the score. Remember that the Z score will be negative.

  • statistics -

    Here mean = 35
    s.d.= 4

    we have asked that
    P(z)=0.98
    see normal table
    It is z=2.05
    remember it is standard normal table value but we have to convert it for x variable for which mean is 35 and s.d. is 4.
    do the inverse operation for which we convert x into z.
    i.e.
    x=mean+z*s.d.
    x=35+2.05*4
    x=47.3
    rounding off it will be 48.

    That is answer is 48.

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