Work Time Lost due to Accidents At a large company, the DIirector of Research found that the average work time los 102 hours per year. She used a random sample of 17 employees. The standard deviation of the sample was 5.5 hours.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![### Work Time Lost due to Accidents
**Scenario:**
At a large company, the Director of Research found that the average work time lost by employees due to accidents was 102 hours per year. She used a random sample of 17 employees. The standard deviation of the sample was 5.5 hours.
**Problem Statement:**
Estimate the population mean for the number of hours lost due to accidents for the company, using a 99% confidence interval. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.
**Instructions:**
1. Determine the estimated range for the population mean (µ).
2. Note: The expression for the confidence interval is typically in the form \( \bar{x} \pm t \frac{s}{\sqrt{n}} \), where:
- \( \bar{x} \) = sample mean
- \( t \) = t-value from the t-distribution table (based on degrees of freedom and confidence level)
- \( s \) = sample standard deviation
- \( n \) = sample size
### Provide Your Answer:
- Range for the population mean (µ) using the 99% confidence interval.
**Please fill in the following boxes with your results:**
\[ < \mu < \]
\[ \boxed{\quad} \]
**Note:**
- Make sure to round intermediate values to at least three decimal places.
- Round final answers to the nearest whole number.
- Click "Submit Answers" when you are finished.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0820f3-64e4-4dfd-b401-c1fa00677880%2F14220f3c-b880-463b-ac12-2f6ded84e4ac%2Fqlek99m_processed.jpeg&w=3840&q=75)
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