The length of useful lifea flourecent tube used for indoorgardening is normally

Question

The length of useful lifea flourecent tube used for indoorgardening is normally distributed. The useful life has a mean of600 hrs and a standard deviation of 40 hrs. determine theprobability that 1. a tube chosen at random will last between 620 and 680hrs 2. such a tube with last more than 740 hrs. 3. such a tube with last less than 740 hrs. 4. a tube chosen at random will last less than 480 hrs or morethan 720 hrs. The length of useful lifea flourecent tube used for indoorgardening is normally distributed. The useful life has a mean of600 hrs and a standard deviation of 40 hrs. determine theprobability that 1. a tube chosen at random will last between 620 and 680hrs 2. such a tube with last more than 740 hrs. 3. such a tube with last less than 740 hrs. 4. a tube chosen at random will last less than 480 hrs or morethan 720 hrs.

Explanation / Answer

1. a tube chosen at random will last between 620 and 680hrs
P(620<X<680) = P((620-600)/40 <Z<(680-600)/40) =P(0.5<Z<2)= 0.2858 (check normaltable)

2. such a tube with last more than 740 hrs.
P(X>740) = P(Z>(740-600)/40) = P(Z>3.5)= 0.0002 (check normal table)

3. such a tube with last less than 740 hrs.
P(X<740)=1-P(X>740)=1-0.0002=0.9998

4. a tube chosen at random will last less than 480 hrs or morethan 720 hrs.

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