Math Answers

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   

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 suvived beyond 3 years, while only 10% of those started by non-graduates are successful.

a. What is the probability that a new SME is successfull

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

c. If it is know that a new SME is successful, what is the probability that it was not started by a graduatre

How would you use a teacher-centered media resource to explain the meaning of ( 7 x 9) to a grade 5 learner. Use two different illustrations to show your understanding.

When three coins are tossed,the probability distribution for the random variable x representing the number of heads that occurs is given below compute the variance and standard deviation of the probability distribution

A problem in a test given to small children asks them to match each of three pictures

of animals to the word identifying that animal. If a child assigns the three words at

random to the three pictures, find the probability distribution for Y , the number of

correct. matches

Calculate the following:

1.1.1(-39)⁰

1.1.2 (9)^5/7 rounded off to 3 significant figures

1.1.3 -5 +3 ÷ 2

1.1.4 -(-32)⁰

1.2 Find the value for the expression (x²)³ / x⁵

Trace the curve 𝑦 = 8/4-x^2 , and state all the properties you use to trace it.