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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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 )
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so to find P(X<2050)
find z value=2050-2000(which is the mean)/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
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