Basic Statistics208210 marksNumerical: Normal distribution income estimationStandard normal distribution and Z-scores
The distribution of monthly incomes of 5,000 employees of a certain industrial unit was found to be normally distributed with mean of Rs. 2,000 and a standard deviation of Rs. 200.(i) Estimate the range of incomes of the middle 60% employees.(ii) Estimate the lowest income of richest 10% employees.(
The distribution of monthly incomes of 5,000 employees of a certain industrial unit was found to be normally distributed with mean of Rs. 2,000 and a standard deviation of Rs. 200.(i) Estimate the range of incomes of the middle 60% employees.(ii) Estimate the lowest income of richest 10% employees.(iii) Estimate the highest income of poorest 10% employees.[10+0+0+0]
- Number of employees: $N = 5000$ - Distribution: Normal - Mean: $\mu = 2000$ - Standard deviation: $\sigma = 200$ Standardization: $Z = \dfrac{X - \mu}{\sigma}$, so $X = \mu + Z\sigma$. --- Middle 60% leaves 20% in each tail. - Lower cut-off: cumulative area $= 0.20 \Rightarrow z1 = -0.84$ - Upp...