Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.9 computers. 16 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N 4.6 0.9 08 b. What is the distribution of ? - N 4.6 0.225 ✓ or or c. What is the distribution of Σx? Σx - N( 73.6 3.6 d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.7 computers per hour. 0.1309 X e. For the 16 workers, find the probability that their average number of computers put together per hour is between 4.4 and 4.7. 0.4833 X f. Find the probability that a 16 person shift will put together between 72 and 75.2 computers per hour. 0.3400 X g. For part e) and f), is the assumption of normal

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### Statistical Analysis of Computer Assembly Workers' Productivity

Each worker at a computer factory can assemble an average of 4.6 computers per hour, with a standard deviation of 0.9 computers per hour. A group of 16 workers is randomly selected to work the next shift. This analysis uses a normal distribution to answer each question and rounds answers to four decimal places where possible.

#### a. Distribution of Individual Worker Productivity

**Question:** What is the distribution of \( X \)?

**Answer:** \( X \sim \mathcal{N}(4.6, 0.9) \)

#### b. Distribution of Average Productivity for 16 Workers

**Question:** What is the distribution of \( \bar{x} \)?

**Answer:** \( \bar{x} \sim \mathcal{N}(4.6, 0.225) \)

#### c. Distribution of Total Productivity for 16 Workers

**Question:** What is the distribution of \( \sum x \)?

**Answer:** \( \sum x \sim \mathcal{N}(73.6, 3.6) \)

#### d. Probability for One Worker to Assemble Between 4.4 and 4.7 Computers

**Question:** If one randomly selected worker is observed, find the probability that this worker will assemble between 4.4 and 4.7 computers per hour.

**Answer:** 0.1309 (Incorrect as per the validation marks in the image)

#### e. Probability for 16 Workers' Average Productivity to be Between 4.4 and 4.7 Computers

**Question:** For the 16 workers, find the probability that their average number of computers assembled per hour is between 4.4 and 4.7.

**Answer:** 0.4833 (Incorrect as per the validation marks in the image)

#### f. Probability for 16 Workers' Total Productivity to be Between 72 and 75.2 Computers

**Question:** Find the probability that a 16-person shift will assemble between 72 and 75.2 computers per hour.

**Answer:** 0.3400 (Incorrect as per the validation marks in the image)

#### g. Assumption of Normal Distribution

**Question:** For parts e) and f), is the assumption of normal distribution necessary?

**Answer:** Yes

#### h. Productivity Threshold for Top 20% Performance

**Question:** A sticker that says "Great Ded
Transcribed Image Text:### Statistical Analysis of Computer Assembly Workers' Productivity Each worker at a computer factory can assemble an average of 4.6 computers per hour, with a standard deviation of 0.9 computers per hour. A group of 16 workers is randomly selected to work the next shift. This analysis uses a normal distribution to answer each question and rounds answers to four decimal places where possible. #### a. Distribution of Individual Worker Productivity **Question:** What is the distribution of \( X \)? **Answer:** \( X \sim \mathcal{N}(4.6, 0.9) \) #### b. Distribution of Average Productivity for 16 Workers **Question:** What is the distribution of \( \bar{x} \)? **Answer:** \( \bar{x} \sim \mathcal{N}(4.6, 0.225) \) #### c. Distribution of Total Productivity for 16 Workers **Question:** What is the distribution of \( \sum x \)? **Answer:** \( \sum x \sim \mathcal{N}(73.6, 3.6) \) #### d. Probability for One Worker to Assemble Between 4.4 and 4.7 Computers **Question:** If one randomly selected worker is observed, find the probability that this worker will assemble between 4.4 and 4.7 computers per hour. **Answer:** 0.1309 (Incorrect as per the validation marks in the image) #### e. Probability for 16 Workers' Average Productivity to be Between 4.4 and 4.7 Computers **Question:** For the 16 workers, find the probability that their average number of computers assembled per hour is between 4.4 and 4.7. **Answer:** 0.4833 (Incorrect as per the validation marks in the image) #### f. Probability for 16 Workers' Total Productivity to be Between 72 and 75.2 Computers **Question:** Find the probability that a 16-person shift will assemble between 72 and 75.2 computers per hour. **Answer:** 0.3400 (Incorrect as per the validation marks in the image) #### g. Assumption of Normal Distribution **Question:** For parts e) and f), is the assumption of normal distribution necessary? **Answer:** Yes #### h. Productivity Threshold for Top 20% Performance **Question:** A sticker that says "Great Ded
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