A random sample of 100,000 credit sales in a department store showed an average sale of $83.25. From past data, it is known that the standard deviation of the population is $25.00. The standard error is 0.07906. With a 0.95 probability, determine the margin of error. O 0.0005 0.0221 0.1549 48.9991
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![**Example Problem: Calculating Margin of Error**
A random sample of 100,000 credit sales in a department store showed an average sale of **$83.25**. From past data, it is known that the standard deviation of the population is **$25.00**. The standard error is **0.07906**. With a 0.95 probability, determine the margin of error.
**Options:**
- 0.0005
- 0.0221
- 0.1549
- 48.9991
**Explanation:**
This problem is about determining the margin of error for a sample mean. The key components provided are:
- Sample mean (\(\bar{x}\)): $83.25
- Population standard deviation (\(\sigma\)): $25.00
- Standard error (SE): 0.07906
- Confidence level: 95%
Using these elements, apply the formula for margin of error as follows:
\[ \text{Margin of Error} = Z \times \text{SE} \]
Where \( Z \) is the Z-score corresponding to a 95% confidence level (typically 1.96 for a two-tailed test).
Here, the correct option is not marked. Calculations would further determine the outcome by plugging in the values. However, none of the provided answer options correctly match typical margin of error calculations for typical confidence intervals unless confirmed differently through context-specific methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffae7c33e-d978-40f5-9f98-38011beb158f%2Fd929511a-066f-47ab-8448-73465d50ba20%2Faagyoma_processed.png&w=3840&q=75)
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