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

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