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Chapter 23: Problem 7

Out of 6000 components, 39 fail within 12 months of manufacture. (a) Calculate the probability that a component picked at random fails within 12 months of manufacture. (b) A batch contains 2000 components. How many of these would you expect to fail within 12 months?

Short Answer

Expert verified
Answer: 13 components are expected to fail within 12 months in a batch of 2000 components.

Step by step solution

01

Calculate the probability of a single component failing within 12 months of manufacture

To calculate this probability, we will divide the number of failed components (39) by the total number of components (6000). Using the formula: Probability of failure = Failed components / Total components P(failure) = \frac{39}{6000} Calculating this probability, we get: P(failure) = \frac{39}{6000} = 0.0065 The probability of a single component failing within 12 months of manufacture is 0.0065.
02

Calculate the expected number of failures in a batch of 2000 components

To calculate the expected number of failures in a batch of 2000 components, we'll use the calculated probability of failure, and multiply it by the total number of components in the batch (2000). In this case, we have: Expected failures = P(failure) * Total components in the batch Expected failures = 0.0065 * 2000 Calculating the expected number of failures, we get: Expected failures = 0.0065 * 2000 = 13 Thus, we would expect 13 components to fail within 12 months in a batch of 2000 components.

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Most popular questions from this chapter

The probability that a component fails within a month is \(0.009\). If 800 components are examined calculate the probability that the number failing within a month is (a) nine, (b) five, (c) less than three, (d) four or more.

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