Answer:
The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.
Explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we select appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,

And the standard deviation of the distribution of the sum of values of X is given by,

The information provided is:
μ = $970
σ = $129
n = 102
Since the sample size is quite large, i.e. n = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.
Then,

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:


*Use a z-table for the probability.
Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.