# Understanding Statistical Probabilities of Observing Events

1. Assume that company A makes 80% of all electrocardiograph machines, company B make 15% of them, and the company C makes the other 5%. The electrocardiographs machines made by company A have a 4% rate of defects, the company B machines have a 5% rate of defects, while the company C machines have a 8% rate of defects.

a) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the probability that is was made by company A.

b) If a randomly selected electrocardiograph machine is then tested and is found to be defective, find the probability that it was made by the com¬pany A.

c) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the probability that it was made by company A and it is defective.

d) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the probability that is was made by company A but it is not defective.

2. Police report that 88% of drivers stopped on suspicion of drunk driving are given a breath test, 15% a blood test, and 10% both tests. What is the probability that the next driver stopped on suspicion of drunk driving is given

i) at least one of the tests?

ii) a blood test or a breath test, but not both?

iii) neither test?

iv) Consider the two events given a blood test and given a breath test. Are the events independent? Are these disjoint events?

https://brainmass.com/statistics/probability/understanding-statistical-probabilities-observing-events-215385

#### Solution Preview

1. Assume that company A makes 80% of all electrocardiograph machines, company B make 15% of them, and the company C makes the other 5%. The electrocardiographs machines made by company A have a 4% rate of defects, the company B machines have a 5% rate of defects, while the company C machines have a 8% rate of defects.

Let A be the event that company A makes a randomly selected machine

Let B be the event that company B makes a randomly selected machine

Let C be the event that company C makes a randomly selected machine

Let D be the event that a randomly selected machine is defective

The information given in the problem is summarized in the table ...

#### Solution Summary

The probability of observing events is understood in the solution. Health applications are examined.

Statistics: understanding z-scores and probabilities of observing events.

I would like some help with the following problems. Can I please get the actual manual work for the problems so I can follow the formula and follow the steps with other word problems. Thanks.

1. A normal population has a mean of 20.0 and a standard deviation of 4.0.

a. compute the z value associated with 25.0.

b. what proportion of the population is between 20.0 and 25.0?

c. what proportion of the population is less than 18.0?

2. The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $70,000 and a standard deviation of $20,000. A loan application is received this morning.

What is the probability.

a. the amount requested is $80,000 or more?

b. the amount requested is between $65,000 and $80,000?

c. the amount requested is $65,000 or more?

3. A study found that a mean waiting time to see a physician at an outpatient clinic was 40 minutes with a standard deviation of 28 minutes. a. what is the probability of more than an hours wait.

b. less than 20 minutes.

c. at least 10 minutes.

4. the credit score of a 35 yr old applying for a mortgage at Ulysses Mortgage Associates is normally distributed with a mean of 600 and a standard deviation of 100.

a. find the credit score that defines the upper 5 percent.

b. seventy-five percent of the customers will have a credit score higher than what value?

c. within what range would the middle 80 percent of credit scores lie.