Statistics and Probability Answers

Buoyancy aids in watersports are tested by adding increasing weights until they sink. A

club has two sets of buoyancy aids. One set is two years old, and should support weights

according to 𝑁(6.0,0.64)kg, the other set is five years old and should support weights of

𝑁(4.5, 1.0) kg. all the aids are tested and any which are unable to spport at least 5kg are

thrown out.

a. If there are 24 two-year aids, how many are still usable?

b. If there are 32 five-year old aids how many are still usable?

QUESTION III

A short term insurance company receives three motor vehicle claims, on average, per day. Assume that

the daily claims follow a Poisson process.

Required:

a) What is the probability that at most two motor vehicle claims are received in any given day?

b) What is the probability that more than two motor vehicle claims are received in any given period

of two days?

An insurance company found that 45% of all insurance policies are terminated before their maturity

date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a

Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

Given μ = -10, σ = 5, n=500, find 𝜇𝑋̅ and 𝜎 2 𝑋̅ Solution

Given μ = -10, σ = 5, n=500, find 𝜇𝑋̅ and 𝜎 2 𝑋̅ Solutio

The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet. Find a 90% confidence interval for the population mean amount of material used in a custom sail.

1. Point estimate value = 
2. Standard error (approximate to four decimal points) = 
3. Margin of error (approximate to four decimal points) = 
4. Tabulated value (approximate to four decimal points) = 
5. Upper limit (approximate to four decimal points) = 
6. Lower limit (approximate to four decimal points) = 

QUESTION III   

A short term insurance company receives three motor vehicle claims, on average, per day. Assume that 

the daily claims follow a Poisson process.

Required:

a) What is the probability that at most two motor vehicle claims are received in any given day?

b) What is the probability that more than two motor vehicle claims are received in any given period 

of two days?

QUESTION II   

An insurance company found that 45% of all insurance policies are terminated before their maturity 

date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a 

Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

UESTION I  

Research has shown that 55% of new Small Medium Enterprises (SMEs) are started by graduates while 

45% are started by non-graduates. It is also known that 70% of SMEs started by graduates are successful 

i.e. they survive beyond 3 years, while only 10% of those started by non-graduates are successful.

Required:

a) What is the probability that a new SME is successful?

b) What is the probability that a new SME is successful and it was not started by a graduate?

c) If it is known that a new SME is successful, what is the probability that it was not started by a 

graduate? 

QUESTION II   

An insurance company found that 45% of all insurance policies are terminated before their maturity 

date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a 

Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

QUESTION III