Final answer:
To find the number of businesses with sales of Rs 40,000, calculate the z-score using the mean and standard deviation, then use the standard normal distribution table to find the corresponding probability and multiply by the total number of businesses.
Step-by-step explanation:
The question at hand involves the application of normal distribution and probability concepts in statistics to find out the number of businesses with sales of Rs 40,000.
To solve this problem, we would use the z-score formula:
Z = (X - μ) / σ
Where:
X = the sales amount of interest (Rs 40,000),
μ = mean average sales (Rs 36,000),
σ = standard deviation of sales (Rs 10,000).
Calculating the z-score for Rs 40,000 sales:
Z = (40,000 - 36,000) / 10,000 = 0.4
We would then look up the z-score on a standard normal distribution table to find the probability of a business having sales less than or equal to Rs 40,000 and subtract the probability of businesses having sales less than Rs 36,000. Since we're dealing with a normally distributed variable, the probability associated with a z-score of 0.4 can be found on the standard normal table. The resulting difference would give us the proportion of businesses between Rs 36,000 and Rs 40,000 sales out of the 500 businesses the officer deals with. Multiplying the proportion by the total number of businesses (500) gives us the actual number of businesses with sales of Rs 40,000.