# Probability of Light Bulb Lifespan: Normal Distribution with Mean 400 Days

• recoil33
In summary, the life of a light bulb manufactured by a company is normally distributed with a mean of 400 days and a standard deviation of 75 days. To find the probability of a randomly chosen bulb lasting at least 450 days, the distribution needs to be standardized using the given mean and standard deviation. Similarly, to find the probability of a bulb lasting less than 150 days, the distribution needs to be standardized as well. This can be done using tables that provide P(Z) values where Z=(X-μ)/σ.
recoil33
The life of a light bulb manufactured by a company is found to be normally distributed. if the bulbs last 400 days with a standard deviation of 75 days, what is the probability that a randomly chosen light bulb lasts?

a) at least 450 days?
b) less than 150 days?
etc.

Throughout the examples in the book I am studying, i am not making much sense of this.
Would be appreciated for some advice were to start.

Thanks

recoil33 said:
The life of a light bulb manufactured by a company is found to be normally distributed. if the bulbs last 400 days with a standard deviation of 75 days, what is the probability that a randomly chosen light bulb lasts?

a) at least 450 days?
b) less than 150 days?
etc.

Throughout the examples in the book I am studying, i am not making much sense of this.
Would be appreciated for some advice were to start.

Thanks

You can say that the 400 is the mean. They gave you the standard deviation, so you can find the variance.

Then you just need to 'standardize' the distribution as tables will give you P(Z) where Z=(X-μ)/σ

Well thank makes it a bit more clear, Thanks for that.

## 1. What is the probability of a light bulb lasting exactly 400 days?

The probability of a light bulb lasting exactly 400 days depends on the shape of the normal distribution curve. The probability of any specific value on a normal distribution curve is infinitesimally small, so the likelihood of a light bulb lasting exactly 400 days is very low.

## 2. What is the average lifespan of a light bulb based on this normal distribution?

The mean or average lifespan of a light bulb based on this normal distribution is 400 days. This means that the most common or expected lifespan for a light bulb is 400 days.

## 3. What is the standard deviation for this normal distribution?

The standard deviation for this normal distribution represents the spread of data around the mean. In this case, the standard deviation is not specified, so it is not possible to determine the exact value. However, it can be assumed that the standard deviation is relatively small, meaning that most light bulbs will have a lifespan close to the mean of 400 days.

## 4. Can we predict when a light bulb will burn out based on this normal distribution?

While the normal distribution can give us an idea of the expected lifespan of a light bulb, it cannot predict exactly when a light bulb will burn out. Probability can only give us a general idea of what to expect, but it cannot be used to make precise predictions for individual cases.

## 5. Are there any factors that can affect the lifespan of a light bulb and change this normal distribution?

Yes, there are several factors that can affect the lifespan of a light bulb and change the normal distribution. These factors include the quality of the light bulb, frequency of use, voltage fluctuations, and environmental conditions such as temperature and humidity. These factors can cause the distribution to shift, making the average lifespan of a light bulb either longer or shorter than 400 days.

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