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anonymous

  • one year ago

The life expectancy of a typical lightbulb is normally distributed with a mean of 2,000 hours and a standard deviation of 27 hours. What is the probability that a lightbulb will last between 1,975 and 2,050 hours? all I know about this question is that I have to use a z-score

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  1. anonymous
    • one year ago
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    @dan815

  2. anonymous
    • one year ago
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    @Preetha

  3. anonymous
    • one year ago
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    Here, we want to know the probability that bulb falls between and 1975 and 2050. The "trick" to solving this problem is to realize the following: P( 1975 < X < 2050 ) = P( X < 2050 ) - P( X < 1975 ) |dw:1435247712590:dw|

  4. anonymous
    • one year ago
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    so to find P(X<2050) find z value=2050-2000(which is the mean)/27 =50/27 look up this z value in the z table and u get the probability of a bulb having life expectancy less than 2050 similarly calculate it for bulb having life expectancy less than 1975 subtract both of them and u get the answer

  5. anonymous
    • one year ago
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    I dont have a z-table :(

  6. anonymous
    • one year ago
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  7. anonymous
    • one year ago
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    is it .2054?

  8. anonymous
    • one year ago
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  9. anonymous
    • one year ago
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    okay so z value for 2050 comes out to be 1.85 so if u look in the table , the value corresponding to 1.85 is 0.9678 so the prob =0.9678

  10. anonymous
    • one year ago
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    now calculate P(X<1975)

  11. anonymous
    • one year ago
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    How would I calculate that? P((0.9678)<1975) ? @nitishdua31

  12. anonymous
    • one year ago
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    oh no, 0.96 is the probability of a bulb having life expectancy less than 2050 now you have to calculate the probability of a bulb having life expectancy less than 1975

  13. anonymous
    • one year ago
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    Ohhhhhhhh gotcha

  14. anonymous
    • one year ago
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    coz when you subtract them , you get the probability of the bulb having life expectancy between them

  15. anonymous
    • one year ago
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    0.17619 0.32381 0.79165 0.96784 that bottom answer looks like the one you gave earlier

  16. anonymous
    • one year ago
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    these are the choices @nitishdua31

  17. anonymous
    • one year ago
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    @dan815 can you help explain ?

  18. anonymous
    • one year ago
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    I'm so lost right now @nitishdua31

  19. anonymous
    • one year ago
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  20. anonymous
    • one year ago
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    take a look at this the first figure shows what you have to calculate, and we can find that by subtracting second and third figure now, we already calculated second, i.e. 0.96 now we have to calculate third

  21. anonymous
    • one year ago
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    the third being the bottom?

  22. anonymous
    • one year ago
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    yes

  23. anonymous
    • one year ago
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    which represents less than 1975

  24. anonymous
    • one year ago
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    I got 75

  25. anonymous
    • one year ago
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    @ganeshie8 can u help ?

  26. anonymous
    • one year ago
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    0.5 for the Z? @nitishdua31

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