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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 ______ _________ ______ ___ _________ ________.
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