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# Probability of Occurrence

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Problem 1
Eighteen (18) people in a department of 162 are fully trained in CPR and AED. A person shows signs of a heart attack. Five (5) people respond. What is the probability that NO (0) person who responded is trained to treat the victim? (Show all of your calculations)

Problem 2
An airline company claims their arrivals are on time within an average of +/- 5 minutes and a standard deviation of 2.82 minutes; Normally Distributed. You sample 50 arrivals and find an average of 6.3 minutes late. Can you be at least 90% sure that the airline company's claim is correct? (Show all of your calculations)

https://brainmass.com/statistics/hypothesis-testing/probability-of-occurrence-141216

#### Solution Preview

Problem 1
Here we know that P(Trained) = 18/162=0.1111
So p=0.1111 q=1-0.1111=0.8889
This is binomial distribution we need to calculate P(r=0, n=5) = 5C0*p^0*q^5
=1*0.1111^0*0.8889^5
=0.554963641 or 0.5550

Problem 2
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