Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 14 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.20 gram.
(a)
Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)
lower limit
upper limit
(b)
What conditions are necessary for your calculations? (Select all that apply.)
normal distribution of weightsn is largeuniform distribution of weightsσ is unknownσ is known
(c)
Interpret your results in the context of this problem.
We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.
(d)
Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
In: Statistics and Probability
Nowadays, movies can be rented from a vending machine located at the entrance to many stores. Suppose that it is now Friday evening at 8pm and a certain machine within a certain store has six copiesof the movie “Twilight” available for rent. The machine will not be visited by the owner until Sunday afternoon at noon (which is 40hrs later), at which time returned movies will be restocked.
Suppose that customers wanting to rent “Twilight” arrive at this rental machine at a rate of 1 every 5 hours.
LetW= the time (in hours) until the next “Twilight” renter arrives at the machine.
Name the distribution of Wand identify the parameter.
Distribution name: ___________________
Parameter value: ___________________
What is the chance the next “Twilight” renter arrives sometime on Saturday?
Thus, we seek the P( ___ < W< ___ ) which equals ________________?
LetX= the number of renters wanting “Twilight” that come to the
vending machine over the weekend (Fri 8pm until Sunday noon).
Name the distribution of Xand identify the parameter.
Distribution name: ___________________
Parameter value: ___________________
What is the probability that exactly 4 copies of “Twilight” are rented over
the weekend? Thus, we seek the P(X= 4) which equals ________________?
What is the probability that all copies of “Twilight” are rented over the
weekend? Thus, we seek P( X __ __ ) which equals ________________?
In: Math
Determine whether the distribution is a discrete probability distribution. If not, state why.
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x |
P(x) |
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0 |
0.1 |
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1 |
0.5 |
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2 |
0.05 |
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3 |
0.25 |
|
4 |
0.1 |
In: Statistics and Probability
What are independent trials, and how do they relate to the definition of probability?
In: Statistics and Probability
Which of the following are TRUE? Select all that apply.
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A probability of 1 is the same as a probability of 100% |
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The difference between interval and ordinal data is that interval data has a natural zero. |
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If you are doing a study and the population is Americans, the easiest type of study to run would be a simple random sample. |
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If your population is 80% female and your sample is 60% male, there is undercoverage bias. |
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In order to calculate a mean on Excel, we type in "=MEAN". |
In: Statistics and Probability
An insurance company estimates the probability of an earthquake in the next year to be 0.0014. They estimate the average damage done by an earthquake to be $60,000. The company offers earthquake insurance for $100 per year, and when damage occurs, the company pays the full price to the customer. Suppose you are working for the company and want to plan for their future finicalness.
A. What is the expected value of the insurance company's pay out to a customer in a year?
B. What is the expected value of the insurance company's profit from each customer in a year?
In: Statistics and Probability
You own a house that is valued at $500,000. The probability of a house fire in your area is 0.0002, and if a house fire happens, your home’s value will be reduced to $0. You are considering buying an insurance for your house. In case of fire, the insurance company will pay you $300,000. Ignore depreciation, taxes, etc. of your house in the following calculations. What is the expected values of your home without insurance and your home if the insurance is free?
In: Statistics and Probability
You own a house that is valued at $500,000. The probability of a house fire in your area is 0.0002, and if a house fire happens, your home’s value will be reduced to $0. You are considering buying an insurance for your house. In case of fire, the insurance company will pay you $300,000. Ignore depreciation, taxes, etc. of your house in the following calculations. Suppose you are a risk-neutral person, what would be the most you are willing to pay for the insurance that pays you $300,000 in case of fire. Please explain your answer.
In: Statistics and Probability
Examine the usage of statistics and probability in vocations such as gambling and insurance. Be sure to include boot-strap methods of prediction, the law of large numbers, and certainty and uncertainty in your response.
In: Statistics and Probability
An insurance company estimates that the probability that a person’s car will be destroyed and need to be replaced in any given year is 0.03. The insurance company charges $2000 for the insurance policy, and if your car is destroyed, they will give you $25000 to buy a replacement car. Let X be the net earnings for the insurance company from one insurance policy. What is the expected net earnings for this insurance company? On average, will the insurance company tend to earn money or lose money?
In: Statistics and Probability