Question

In: Statistics and Probability

A bulletproof vest manufacturer has 1000 bulletproof vests for sale. Each vest has a 5% probability...

A bulletproof vest manufacturer has 1000 bulletproof vests for sale. Each vest has a 5% probability of experiencing a failure resulting in a serious injury or death. You randomly select 200 vests for potential purchase.

What is the likelihood that 10 vests will experience a failure resulting in a serious injury or death? [Show your work]

What is the likelihood that they will all be free from defect? [Show your work]

What is the likelihood that they will all experience a failure resulting in serious injury or death? [Show your work]

Solutions

Expert Solution

Sample size = n =200

Probability of failure = p = 0.05

This can be approximated by normal distribution since n is large and

n*p = 200*0.05 =10 and is greater than 5.

The normal approximation is given by:

Mean

Variance :

= 3.08211

What is the likelihood that 10 vests will experience a failure resulting in a serious injury or death?

The probability that 10 vests fail out of 200 is given by:

Applying continuity correction,

=0.5636 - 0.4364

=0.1272

The likelihood that 10 vests will experience a failure resulting in a serious injury or death is 0.1272.

What is the likelihood that they will all be free from defect?

Probability that all vests are free of defect is given by

=0.0010-0.0003

=0.0007

The likelihood that all vests will be free from defect is 0.0007.

What is the likelihood that they will all experience a failure resulting in serious injury or death?

Probability that all vests experience a failure resulting in serious injury or death is given by:

61.484< Z< 61.8085

0.0000

The likelihood that all vests experience a failure resulting in serious injury or death is is 0.0000.

orchestra answered 1 year ago

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