e average annual premium for automobile insurance in the United States is $1543. A representative sample of annual premiums for the state of Michigan is contained in the Excel Online file below. Assume the population is approximately normal. Construct a spreadsheet to answer the following questions.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
The average annual premium for automobile insurance in the United States is $1543. A representative sample of annual premiums for the state of Michigan is contained in the Excel Online file below. Assume the population is approximately normal. Construct a spreadsheet to answer the following questions.
![Annual
Premium
Formula Used
1909
Sample Size
2570.55
=SUM(A2:A21)/20
3198
2321
Point Estimate of Mean (to the whole)
#N/A
2708
2589
Standard Deviation (4 decimals)
#N/A
2999
2687
Confidence Coefficient
0.95
2575
2615
Level of Significance
#N/A
2680
2334
Margin of Error (2 decimals)
#N/A
2897
C.I. Lower Limit (2 decimals)
C.I. Upper Limit (2 decimals)
2940
#N/A
2571
#N/A
2608
2183
National Average for the U.S.
1543
2590
2146
the annual automobile insurance
#N/A
2380
premium in Michigan include the
national average for the United
States?
2481](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5322f76-08be-4cea-9041-3fbbc034811a%2F6d05993a-8a88-44d4-a120-caed998f384b%2Fzi8abyb_processed.jpeg&w=3840&q=75)
![The average annual premium for automobile insurance in the United States is $1543. A representative sample of annual premiums for the state of Michigan is contained in
the Excel Online file below. Assume the population is approximately normal. Construct a spreadsheet to answer the following questions.
Open spreadsheet
a. Provide a point estimate of the mean annual automobile insurance premium in Michigan.
$ 2570.55
(to the nearest dollar)
b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan.
($ 2435.67
$ 2705.43
(to the nearest cent)
c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States?
What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?
We would be
% confident that auto insurance premiums in Michigan are
v the national average.
Check My Work
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