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MTH 120 - Using the Normal Curve

MTH 120 - Using the Normal Curve - center bar 85 hrs(i.e 98...

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Example 3 (page 527) The Eureka Lightbulb Company tested a new line of lightbulbs and found their lifetimes to be normally distributed with a mean life of 98 ( μ = 98) and a standard deviation of 13 hours ( σ = 13). In class we discussed answering question a.: What percentage of bulbs will last less than 72 hours? Here we will discuss answering question b.: What is the probability that a lightbulb selected at random will last longer than 111 hours? First, let’s add the appropriate values to each of the vertical bars on our normal curve: 1. Since we were told the mean is 98 hours, we will label the middle bar 98 hrs, and 2. Since we were told the standard deviation is 13, we will label the 3 bars to the right of the center bar 111 hrs (i.e., 98 + 1x13), 124 hrs (i.e., 98 + 2x13), and 137 hrs (i.e., 98 + 3x13), and the 3 bars to the left of the
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Unformatted text preview: center bar 85 hrs (i.e., 98 – 1x13), 72 hrs (i.e., 98 – 2x13), and 59 hrs (i.e., 98 – 3x13). To answer question b., let’s recognize that a lightbulb selected at random will either burn out: 1. In less than 111 hours, or 2. In more than 111 hours. The probability that a lightbulb selected at random will last longer than 111 hours is: 0.1% + 2.2% + 13.6% = 15.9% … Almost… Since probabilities are reported in decimal form, we would say the probability that a lightbulb selected at random will last longer than 111 hours is: 0.159 Here’s another example: The probability that a lightbulb selected at random will last between 85 and 111 hours is: 0.682; i.e., 0.341 + 0.341 98 hrs 111 hrs 124 hrs 137 hrs 85 hrs 72 hrs 59 hrs...
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MTH 120 - Using the Normal Curve - center bar 85 hrs(i.e 98...

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