# Uses of mean, standard deviation and Z tables

• sazzlefrazzle
In summary, the conversation discusses testing light emitting diodes and determining the guaranteed lifetime that should be listed on the box. The calculations involve using the Z table standard normal distribution and finding X, the lifetime at which the probability of failure is less than or equal to 2%. There is also a question about converting from a normal distribution to a standard normal distribution.

#### sazzlefrazzle

Hey i was wondering if anyone could help me with this question at all? I don't have a clue about the calculations and would be grateful if it could be explained to me! I'm really struggling! Thanks

Some light emitting diodes are tested and a sample is found to have a mean lifetime of 2048 hours and a standard deviation of 40 hours. The manufacturer wants to give a guaranteed lifetime for the LED’s on the box so that only 2% of the bulbs will be returned for not lasting for the guaranteed lifetime. Using Z table standard normal distribution show your calculation giving the lifetime he should put on the box.

The question is asking you to find the lifetime X such that the probability of failure P(F) is less then or equal to .02.

Do you know how to change from a normal distribution with mean $\mu$ and standard deviation $\sigma$ to the standard normal distribution? If not, why in the world are you doing a problem like this?

## 1. What is the mean and how is it used?

The mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding all the values in the data set and dividing by the total number of values. It can be used to summarize and describe the data, and can also be used to compare different data sets.

## 2. How is standard deviation calculated and why is it important?

Standard deviation is a measure of how spread out the data is from the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean. It is important because it allows us to understand the variability or consistency of the data. A smaller standard deviation indicates that the data points are close to the mean, while a larger standard deviation suggests that the data points are more spread out.

## 3. What are Z tables and how are they used?

Z tables, also known as standard normal tables, are a type of statistical table that is used to find the area under the normal curve for a given value of z-score. They are used to calculate probabilities and to perform hypothesis testing in statistics. Z tables are typically used when working with data that is normally distributed.

## 4. How are mean, standard deviation, and Z tables related?

The mean and standard deviation are used to calculate the z-score, which is the number of standard deviations a data point is from the mean. This z-score is then used to find the corresponding probability in the Z table. In other words, the mean and standard deviation provide information about the distribution of the data, while the Z table helps us to interpret and make conclusions about the data.

## 5. Can mean, standard deviation, and Z tables be used in any type of data?

Mean, standard deviation, and Z tables are most commonly used for normally distributed data, but they can also be used for other types of data as long as certain assumptions are met. For example, the data should be continuous and the sample size should be large enough. If these assumptions are not met, alternative methods of analysis may need to be used.