Question Tag: Warranty Calculation

CarJoy Manufacturing Company produces electronic components that have life spans normally distributed with mean $\mu$ hours and standard deviation σ hours. Only 1% of the components have a life span less than 3,500 hours and 2.5% have a life span greater than 5,500 hours.

Required:
i) By standardizing the values of $X$ to the standard normal values, obtain TWO (2) linear equations in $\mu$ and $\sigma$. (4 marks)

ii) Using an appropriate method of solving simultaneous equations, determine the value of $\mu$ and $\sigma$ in (i) above. (4 marks)

iii) Determine the proportion of electronic components with life spans between 4,120.50 hours and 5,052.45 hours. (4 marks)

iv) If the company gives a warranty of 4,000 hours on the components, find the percentage of components the company is expected to replace under the warranty. (4 marks)