Probability of Defective Parts and Machine Failure
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Questions and Answers

What is the probability that a part selected from Line A or Line B is defective?

  • 0.045 (correct)
  • 0.035
  • 0.055
  • 0.050

    • What is the probability that at least one of Machine X or Machine Y fails during a shift?

  • 0.11
  • 0.08
  • 0.10 (correct)
  • 0.09

    • What is the probability that at least one of the two suppliers delivers late?

  • 0.20 (correct)
  • 0.15
  • 0.25
  • 0.18

    • What is the missing probability for the number of defective products when 2 defective products occur?

    <p>0.20</p> Signup and view all the answers

    What is the correct missing probability value for the number of machine breakdowns when 1 breakdown occurs?

    <p>0.30</p> Signup and view all the answers

    How is the mean of the defective products calculated from the provided distribution?

    <p>Using the formula E(X) = Σ [X * P(X)]</p> Signup and view all the answers

    When calculating variance, which formula is used for the distribution of defective products?

    <p>Var(X) = E(X^2) - (E(X))^2</p> Signup and view all the answers

    What is the standard deviation of the defective products based on the calculated variance?

    <p>Square root of the variance</p> Signup and view all the answers

    What is the probability that exactly 1 machine breaks down in a factory of 20 machines, given that the probability of any machine breaking down is 0.04?

    <p>0.218</p> Signup and view all the answers

    What is the probability that at least 2 machines break down on a given day in a factory of 20 machines?

    <p>0.820</p> Signup and view all the answers

    For a batch of 40 parts produced, what is the probability that at most 3 parts are defective, given that the defect rate is 5%?

    <p>0.876</p> Signup and view all the answers

    What is the mean number of late deliveries from a total of 15 deliveries per week where the probability of a delivery being late is 0.10?

    <p>2.0</p> Signup and view all the answers

    What is the standard deviation of the number of parts that are defective in a batch of 40 parts where the defect probability is 0.05?

    <p>1.37</p> Signup and view all the answers

    When considering the deliveries made over a week, what is the variance in the number of late deliveries, given the probability of a late delivery is 0.10?

    <p>1.25</p> Signup and view all the answers

    In the context of a manufacturing company’s production times, what is the median time taken to produce parts?

    <p>15 minutes</p> Signup and view all the answers

    What is the cumulative probability that exactly 3 deliveries are late from a total of 15 deliveries where the probability of a delivery being late is 0.10?

    <p>0.210</p> Signup and view all the answers

    What is the mean of the machine downtime values provided?

    <p>4.0</p> Signup and view all the answers

    Which product type had the least number of defects?

    <p>Product B</p> Signup and view all the answers

    In which month did the Packaging department have more breakdowns?

    <p>Month 2</p> Signup and view all the answers

    What are the values of Q1 and Q3 for the machine downtime data?

    <p>Q1 = 2.8, Q3 = 4.2</p> Signup and view all the answers

    Which shift for Machine A had the highest number of defective products?

    <p>Night</p> Signup and view all the answers

    What is the interquartile range (IQR) for the machine downtime values?

    <p>1.5</p> Signup and view all the answers

    Which department had the most machine breakdowns in total over two months?

    <p>Assembly</p> Signup and view all the answers

    What visualization would best summarize the data for the number of defective products for each product type?

    <p>Bar plot</p> Signup and view all the answers

    Study Notes

    Probability of Defective Parts

    • The probability of a part being defective from either Line A or Line B is calculated by considering the probability of a defective part from each line individually and adding them together.

    Probability of Machine Failure

    • The probability of at least one of Machine X or Machine Y failing during a shift is determined by calculating the probability of both machines failing and the probability of only one machine failing, and adding these probabilities together.

    Probability of Late Deliveries

    • The probability of at least one of the two suppliers delivering late is calculated by considering the probability of both suppliers delivering late and the probability of only one supplier delivering late, and adding these probabilities together.

    Missing Probability for Defective Products

    • The missing probability for the number of defective products when 2 defective products occur is determined by subtracting the sum of the probabilities for the other outcomes from 1.

    Missing Probability for Machine Breakdowns

    • The correct missing probability value for the number of machine breakdowns when 1 breakdown occurs is determined by subtracting the sum of the probabilities for the other outcomes from 1.

    Mean of Defective Products

    • The mean of the defective products is calculated by multiplying the number of defective products by their respective probabilities and summing the results.

    Variance Formula for Defective Products

    • The variance of the defective products is calculated using the formula: Variance = Σ(x^2 * P(x)) - (μ)^2, where x represents the number of defective products, P(x) represents the probability of each outcome, and μ represents the mean.

    Standard Deviation of Defective Products

    • The standard deviation of the defective products is found by taking the square root of the calculated variance.

    Probability of Machine Breakdown

    • The probability of exactly 1 machine breaking down in a factory of 20 machines, given that the probability of any machine breaking down is 0.04, is calculated using the binomial probability formula.

    Probability of Multiple Machine Breakdowns

    • The probability of at least 2 machines breaking down on a given day in a factory of 20 machines is calculated by summing the probabilities of 2, 3, 4 ... up to 20 machines breaking down.

    Probability of Defective Parts in a Batch

    • The probability of at most 3 parts being defective in a batch of 40 parts, given that the defect rate is 5%, is calculated by summing the probabilities of 0, 1, 2, and 3 defective parts.

    Mean Number of Late Deliveries

    • The mean number of late deliveries from a total of 15 deliveries per week where the probability of a delivery being late is 0.10 is calculated by multiplying the total number of deliveries by the probability of a late delivery.

    Standard Deviation of Defective Parts

    • The standard deviation of the number of parts that are defective in a batch of 40 parts where the defect probability is 0.05 is calculated using the formula: Standard Deviation = √(n * p * (1 - p)), where n is the batch size, p is the defect probability, and (1 - p) is the probability of a part not being defective.

    Variance in Late Deliveries

    • The variance in the number of late deliveries over a week, given the probability of a late delivery is 0.10, is calculated using the formula: Variance = n * p * (1 - p), where n is the total number of deliveries and p is the probability of a late delivery.

    Median Production Time

    • The median time taken to produce parts in a manufacturing company is the middle value of the production times when they are arranged in ascending order.

    Cumulative Probability of Late Deliveries

    • The cumulative probability that exactly 3 deliveries are late from a total of 15 deliveries where the probability of a delivery being late is 0.10 is calculated by summing the probabilities of 0, 1, 2, and 3 late deliveries.

    Mean of Machine Downtime

    • The mean of the machine downtime values provided is obtained by summing all the downtime values and dividing the sum by the total number of downtime values.

    Product Type with Least Defects

    • The product type with the least number of defects is determined by comparing the number of defects reported for each product type and identifying the type with the lowest count.

    Department with Most Breakdowns in a Month

    • The month with the highest number of breakdowns in the Packaging department is identified by examining the breakdown data for each month and noting the month with the maximum number of breakdowns.

    Q1 and Q3 for Machine Downtime

    • Q1 and Q3 for the machine downtime data represent the first and third quartiles, respectively. They are the values that divide the ordered data into four equal parts.

    Shift with Highest Defective Products for Machine A

    • The shift for Machine A with the highest number of defective products is determined by comparing the number of defective products produced during each shift and identifying the shift with the maximum count.

    Interquartile Range (IQR)

    • The interquartile range (IQR) for the machine downtime values is the difference between the third quartile (Q3) and the first quartile (Q1).

    Department with Most Breakdowns

    • The department with the most machine breakdowns in total over two months is identified by summing the number of breakdowns for each department over the two months and finding the department with the highest total.

    Visualization for Defective Products

    • A bar chart or a pie chart would be the best visualizations to summarize the data for the number of defective products for each product type. This will allow for the clear comparison of defect frequencies between different product types.

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    Description

    Explore the probabilities of defective parts from two production lines and the reliability of two machines. This quiz covers calculating the probability of defects and machine failures using given statistical formulas. Test your understanding of probability concepts with real-world manufacturing scenarios.

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