Statistics and Probability Answers

A company prices its hurricane insurance using the following assumptions:
i In any calendar year, there can be at most one hurricane.
ii In any calendar year, the probability of a hurricane is 0.05 .
iii The number of hurricanes in any calendar year is independent of the number of hurricanes in any other calendar year.
Using the company’s assumptions, calculate the probability that there are fewer than 3 hurricanes in a 20-year period.

Suppose an airline accepted 12 reservations for a commuter plane with 10 seats. They know that 7 reservations went to regular commuters who will show up for sure. The other 5 passengers will show up with a 50% chance, independently of each other.
(a) Find the probability that the flight will be overbooked. (b) Find the probability that there will be empty seats.

A recent study shows that the annual cost of maintaining a building in Accra averages 200 Cedis with a variance of 260 Cedis. If a tax of 30% is introduced on all items associated with the maintenance of building i.e. everything is made 30% more expensive. Calculate the standard deviation of the annual cost of maintaining a building in Accra

A company prices is hurricane insurance using the following assumptions
i. In any calendar year, there can be at most one hurricane
ii. In any calendar year,the probability of a hurricane is 0.05
iii. The number of hurricanes in any calendar year is independent of the number of hurricanes in any other calendar year.
Using the company’s assumptions, calculate the probability that there are fewer than 3 hurricanes in a 20 year period.

A financial analyst has found out that policy holders are four times as likely to file two claims as to file four claims.If the number of claims filed has Poisson distribution,What is the variance of the number of claims filed.

An archer shoots arrows at a circular target where the central portion of the target inside is called the bull. The archer hits the bull with probability 1/32. Assume that the archer shoots 96 arrows at the target, and that all shoots are independent.

(a) Find the probability mass function of the number of bulls that the archer hits.

(b) Give an approximation for the probability of the archer hitting no more than one Bull

A recent study shows that the annual cost of maintaining a building in Accra averages 200 Cedis with a variance of 260 Cedis. If a tax of 30% is introduced on all items associated with the maintenance of building i.e. everything is made 30% more expensive.
Calculate the standard deviation of the annual cost of maintaining a building in Accra.

1d. The researchers decide to do a two tailed Matched Pairs T-test to decide if there is a significant difference in tire wear. The experiment yields a t-score of 2.1
If they are using an alpha rejection level of 5%, what decision should they make about tire wear? Justify your answer.

1e. If they decide that one tire type wears significantly more than the other, what type of error could they be making and what are the ramifications of that decision.

2d. When checking for independence we often use the 10% rule. Explain why this is necessary.

2e. In this study, the researchers used a random selection of dogs. Is this necessary? Explain in detail when it is necessary to use random subjects and when it is not.

6d. Explain a method of doing this as a matched pairs experiment.

6e. A reviewer is concerned that your matched pairs experiment may have bias in it. Explain what you did or could do to reduce their fear.

A hospital receives 20% of its COVID-19 vaccine shipments from Japan and the
remainder of its shipments from neighbouring countries. Each shipment contains a very large number of vaccine vials. For Japan’s shipments, 10% of the vials are ineffective. For the neighbouring countries, 2% of the vials are ineffective.
The hospital tests 30 randomly selected vials from a shipment and finds that one is ineffective.
What is the probability that the shipment came from Japan ?

An archer shoots arrows at a circular target where the central portion of the target inside is called the bull. The archer hits the bull with probability 1/32. Assume that the archer shoots 96 arrows at the target, and that all shoots are independent
(a) Find the probability mass function of the number of bulls that the archer hits.
(b) Give an approximation for the probability of the archer hitting no more than one bull.