anonymous
  • anonymous
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
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@dan815
anonymous
  • anonymous
@Preetha
anonymous
  • anonymous
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|

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anonymous
  • anonymous
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
anonymous
  • anonymous
I dont have a z-table :(
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
is it .2054?
anonymous
  • anonymous
anonymous
  • anonymous
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
anonymous
  • anonymous
now calculate P(X<1975)
anonymous
  • anonymous
How would I calculate that? P((0.9678)<1975) ? @nitishdua31
anonymous
  • anonymous
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
anonymous
  • anonymous
Ohhhhhhhh gotcha
anonymous
  • anonymous
coz when you subtract them , you get the probability of the bulb having life expectancy between them
anonymous
  • anonymous
0.17619 0.32381 0.79165 0.96784 that bottom answer looks like the one you gave earlier
anonymous
  • anonymous
these are the choices @nitishdua31
anonymous
  • anonymous
@dan815 can you help explain ?
anonymous
  • anonymous
I'm so lost right now @nitishdua31
anonymous
  • anonymous
anonymous
  • anonymous
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
anonymous
  • anonymous
the third being the bottom?
anonymous
  • anonymous
yes
anonymous
  • anonymous
which represents less than 1975
anonymous
  • anonymous
I got 75
anonymous
  • anonymous
@ganeshie8 can u help ?
anonymous
  • anonymous
0.5 for the Z? @nitishdua31

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