4.   Suppose that an insurance company charges $1150 per year to cover a car in a nearby city. Suppose that there are three different scenarios that the company has to consider:
a.   There is a .0005 probability that the policy holder will cause a fatality and the company will pay $1,000,000.
b.   There is a .01 probability that the policy holder will injure someone and the company will pay $20,000.
c.   There is a .1 probability that the policy holder will be in an accident and the company will pay $2,000.
What is the expected value for the policy and is it wise for the company to continue to offer it?

The annual rainfall in a certain region is approximately normally distributed with mean 41.2 inches and standard deviation 5.5 inches. Round answers to at least 4 decimal places.

a) What is the probability that an annual rainfall of less than 44 inches?

b) What is the probability that an annual rainfall of more than 39 inches?

c) What is the probability that an annual rainfall of between 38 inches and 42 inches?

d) What is the annual rainfall amount for the 75th percentile?

The proton is not truly a point particle, but can be modeled as a sphere of radius approx 1 fm. This is an approximation. Calculate the probability that the electron in the ground state of hydrogen will be found within 1.00000 fm of the center of the proton in the following two ways. Talk about the differences or lack of differences between the two results.

a.) Integrate the radial probability density over the appropriate range of radii.

b.) Multiply the appropriate range of radii by the radial probability density evaluated in the center of that interval.

A POLYGRAPH (LIE DETECTOR) IS AN INSTRUMENT USED TO DETERMINE IF AN INDIVIDUAL IS TELLING THE TRUTH. THESE TESTS ARE CONSIDERED TO BE 95 % RELIABLE. IN OTHER WORDS, IF AN INDIVIDUAL LIES, THERE IS A .95 PROBABILITY THAT THE TEST WILL DETECT A LIE. LET THERE ALSO BE A .025 PROBABILITY THAT THE TEST ERRONEOUSLY DETECTS A LIE EVEN WHEN THE INDIVIDUAL IS ACTUALLY TELLING THE TRUTH. CONSIDER THE NULL HYPOTHESIS, "THE INDIVIDUAL IS TELLING THE TRUTH, THE ANSWER THE FOLLOWING QUESTIONS

WHAT IS THE POBABLITY OF A TYPE I ERROR?

WHAT IS THE PROBABILITY OF A TYPE II ERROR

In the EAI sampling problem, the population mean is $51,200 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4238 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table.

1. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)?
     
   
2. What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used (to 4 decimals)?

In the EAI sampling problem, the population mean is $51,100 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4977 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

1. What is the probability that the sample mean is within $600 of the population mean if a sample of size 40 is used (to 4 decimals)?
   
   
2. What is the probability that the sample mean is within $600 of the population mean if a sample of size 80 is used (to 4 decimals)?

A survey reported that the mean starting salary for college graduates after a three-year program was $35,710.Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3320. What percentage of the graduates have starting salaries: (Round z-score computation to 2 decimal places and the final answers to 4 decimal places.) a. Between $31,800 and $39,200? Probability b. More than $43,600? Probability c. Between $39,200 and $43,600? Probability

The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.9

fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected.

​(a) Find the probability that the drink is less than 11.7 fluid ounces.

​(b) Find the probability that the drink is between 11.6 and 11.7 fluid ounces.

​(c) Find the probability that the drink is more than 12.3 fluid ounces.

Can this be considered an unusual​ event? Explain your reasoning.

What is probability, what can it values be, and what those values can mean (i.e. unusual, rare, likely, impossible, certain, uncertain). Also, what are the differences between empirical probability and theoretical probability. Next what is the addition rule and the multiplication rule. How can you tell the difference between them and when to use them? Also, what do the terms mutually exclusive/disjoint and independence and dependence events mean? How do they differ?