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Answer:
The interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.
Step-by-step explanation:
In statistics, the 68–95–99.7 rule, also recognized as the Empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean, respectively.
Then,
- P (µ - σ < X < µ + σ) = 0.68
- P (µ - 2σ < X < µ + 2σ) = 0.95
- P (µ - 3σ < X < µ + 3σ) = 0.997
he random variable X can be defined as the amount of time a certain brand of light bulb lasts.
The random variable X is normally distributed with parameters µ = 1300 hours and σ = 90 hours.
Compute the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:
[tex]P (\mu - \sigma < X < \mu + \sigma) = 0.68\\\\P(1300-90<X<1300+90)+0.68\\\\P(1210<X<1390)=0.68[/tex]
Thus, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.
This question is based on the statistics. Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.
Given:
The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1300 hours and a standard deviation of 90 hours.
According to the question,
As we know that, In statistics, the 68–95–99.7 rule, also called as the Empirical rule states that, for a normal distribution, all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
Therefore,
P (µ - σ < X < µ + σ) = 0.68
P (µ - 2σ < X < µ + 2σ) = 0.95
P (µ - 3σ < X < µ + 3σ) = 0.997
The random variable X can be defined as, the amount of time a certain brand of light bulb lasts and the random variable X is normally distributed with parameters µ = 1300 hours and σ = 90 hours.
Now, calculate the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:
⇒ P ( µ - σ < X < µ + σ ) = 0.68
⇒ P ( 1300 - 90 < X < 1300 + 90 ) = 0.68
⇒ P( 1210 < X < 1390) = 0.68
Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.
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https://brainly.com/question/5286270
