IGNOU MS 8 2026 - The weekly wages of 2000 workmen are normally distributed with mean wa

Question

The weekly wages of 2000 workmen are normally distributed with mean wage of Rs. 70 and wage standard deviation of Rs 5. Estimate the number of workers whose weekly wages are

a) Between Rs 70 and Rs. 71,

b) More than Rs. 72

27 Jan 2026

Answer :

Word Count : 879

To solve this problem, we apply the principles of normal distribution in the context of quantitative analysis for managerial applications. The weekly wages are normally distributed with mean ( \mu = 70 ) and standard deviation ( \sigma = 5 ). The total number of workmen is ( N = 2000 ). We will use the standard normal distribution ( Z ) to calculate the required probabilities and then estimate the number of workers. First, we convert the raw wages into Z-scores using the formula: [ Z = \frac{X - \mu}{\sigma} ] where ( X ) is the wage, ( \mu ) is the mean wage, and ( \sigma ) is the standard deviation. Part (a): Number of workers earning between Rs. 70 and Rs. 71 For ( X = 70 ): [ Z_1 = \frac{70 - 70}{5} = 0 ] For ( X = 71 ): [ Z_2 = \frac{71 - 70}{5} = \frac{1}{5} = 0.2 ] Next, we look up the standard normal table (or use a Z-table) to find the probabilities corresponding to these Z-scores: * ( P(Z \leq 0) = 0.5 ) * ( P(Z \leq 0.2) \approx 0.5793 ) The probability of wages being between Rs. 70 and Rs. 71 is: [ P(70 \leq X \leq 71) = P(Z \leq 0.2) - P(Z \leq 0) = 0.5793 - 0.5 = 0.0793 ] The estimated number of workers in this wage range is: [ \text{Number of workers} = N \times P = 2000 \times 0.0793 \approx 159 ] So, approximately 159

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