Question

In: Statistics and Probability

A home security system is designed to have a 99% reliability rate. Suppose that eleven homes...

A home security system is designed to have a 99% reliability rate. Suppose that eleven homes equipped with this system experience an attempted burglary. Find the probabilities of these events. (Round your answers to three decimal places.) (a) at least one of the alarms is triggered (b) more than nine of the alarms are triggered (c) ten or fewer alarms are triggered

Solutions

Expert Solution

The values provided in the above question are as below

n = 11, p = 0.99

We use Binomial distribution for find probabilities are as below

  

We find the probabilities of following events

(a) at least one of the alarms is triggered

We also write above probability in the following form

Using Binomial distribution

The probability of at least one of the alarms is triggered is 1

(b) more than nine of the alarms are triggered

We also write above probability in the following form

  

  

  

The probability of more than nine of the alarms are triggered is 0.99482

(c) ten or fewer alarms are triggered

We also write above probability in the following form

  

  

  

  

The probability of ten or fewer alarms are triggered is 0.104662

Summary :-

(a) The probability of at least one of the alarms is triggered is 1

(b) The probability of more than nine of the alarms are triggered is 0.99482

(c) The probability of ten or fewer alarms are triggered is 0.104662

orchestra answered 1 year ago
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