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Chapter 7: Problem 37

A time study was conducted by the production manager of Vista Vision to determine the length of time in minutes required by an assembly worker to complete a certain task during the assembly of its Pulsar color television sets. a. Describe a sample space corresponding to this time study. b. Describe the event \(E\) that an assembly worker took 2 min or less to complete the task. c. Describe the event \(F\) that an assembly worker took more than 2 min to complete the task.

Short Answer

Expert verified
The sample space \(S\) for this time study consists of all non-negative real numbers: \(S = \{t \in \mathbb{R} | t \geq 0\}\). Event E represents the assembly worker completing the task in 2 minutes or less: \(E = \{t \in S | 0 \leq t \leq 2\}\). Event F represents the worker taking more than 2 minutes to complete the task: \(F = \{t \in S | t > 2\}\).

Step by step solution

01

Understanding Sample Space, Events, and Probability

In probability theory, a sample space is a set of all possible outcomes or results of a random experiment. We can think of an event as a subset of the sample space. In this problem, the experiment is "measuring the time a worker takes to complete a certain task in the assembly of Pulsar color television sets." The sample space is the set of possible times in minutes it could take a worker to complete the task.
02

Describing the Sample Space

The sample space corresponding to this time study would consist of all non-negative real numbers (since the time to complete a task can be any positive value, including zero and fractions of minutes). We can denote the set of non-negative real numbers by \(S\), where: \[S = \{t \in \mathbb{R} | t \geq 0\}\] In simpler words, the sample space \(S\) contains all times \(t\) in minutes, such that \(t\) can be any non-negative real number.
03

Describing Event E

Event E corresponds to the situation where an assembly worker completed the task in 2 minutes or less. We can describe this event as a subset of the sample space \(S\). The event \(E\) includes all the times \(t\) in the sample space such that \(t\) is between 0 and 2 minutes (inclusive). We can write event E as: \[E = \{t \in S | 0 \leq t \leq 2\}\]
04

Describing Event F

Event F corresponds to the situation where an assembly worker took more than 2 minutes to complete the task. Similar to event E, event F can be described as a subset of the sample space \(S\). The event \(F\) includes all the times \(t\) in the sample space such that \(t\) is greater than 2 minutes. We can write event F as: \[F = \{t \in S | t > 2\}\]

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