Final answer:
The original question about the original price of the phone cannot be answered without additional information on the discount and rebate rates. For the standard deviation question, a hypothesis test could determine whether pricing variance is greater than the manufacturer's claim. As a buyer, a larger standard deviation suggests better deals may be available.
Step-by-step explanation:
To determine if the pricing has a larger standard deviation than claimed by the manufacturer, we can perform a hypothesis test. Assuming the manufacturer's claim of a standard deviation of $25, we can calculate the sample standard deviation of the given prices and compare it at the 5 percent significance level using appropriate statistical methods, such as a chi-square test for variance. However, it appears there is no data in the question regarding a discount or a rebate that pertains to the original price of a cellular phone.
As a potential buyer, a practical conclusion would be based on analyzing the computed standard deviation against the manufacturer's claim. If the calculated standard deviation is significantly larger, it suggests that the variability in pricing is greater than what the manufacturer suggests, indicating that shopping around could yield a better deal.
If you are referring to how to find the original price of the phone with the known final price, discounts, and rebates, the question does not provide enough information for a specific numerical answer, such as the rate of the discount or the amount of the rebate. Generally, you would calculate the original price by back-calculating from the final price, accounting for the rebate and the percentage of the discount applied to the original price.