5. A random variable \(X\) has a normal distribution.
- Describe two features of the distribution of \(X\).
A company produces electronic components which have life spans that are normally distributed. Only \(1 \%\) of the components have a life span less than 3500 hours and \(2.5 \%\) have a life span greater than 5500 hours.
- Determine the mean and standard deviation of the life spans of the components.
The company gives warranty of 4000 hours on the components.
- Find the proportion of components that the company can expect to replace under the warranty.