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Chapter 7: Problem 34

The manager of a local bank observes how long it takes a customer to complete his transactions at the automatic bank teller. a. Describe an appropriate sample space for this experiment. b. Describe the event that it takes a customer between 2 and 3 min to complete his transactions at the automatic bank teller.

Short Answer

Expert verified
a. The sample space S for this experiment can be represented as an interval of non-negative numbers, including zero up to positive infinity: \[S = [0, +\infty)\] b. The event E, where a customer takes between 2 and 3 minutes to complete a transaction at the automatic bank teller can be written as: \[E = [2,3]\]

Step by step solution

01

Understand the sample space

The sample space is the set of all possible outcomes of an experiment. In this case, the sample space consists of all the possible times it could take a customer to complete a transaction at the automatic bank teller.
02

Represent the sample space

Since the time can be any non-negative number, we can represent the sample space as an interval starting from 0 to positive infinity. Mathematically, the sample space (denoted by 'S') can be written as: \[S = [0, +\infty)\] This means that the sample space includes all non-negative numbers (including zero) up to positive infinity. b. Describe the event that it takes a customer between 2 and 3 min to complete his transactions at the automatic bank teller.
03

Understand the event

An event is a subset of the sample space, representing one or more outcomes that satisfy a certain condition. In this case, the condition is that it takes a customer between 2 and 3 minutes to complete the transaction.
04

Represent the event

The event in question can be represented as a subset of the sample space, in the form of an interval that includes all numbers between 2 and 3 minutes. Mathematically, the event (denoted by 'E') can be written as: \[E = [2,3]\] This means that the event includes all the transaction times between 2 and 3 minutes, inclusive of the endpoints 2 and 3 minutes.

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