Math Answers

A scientist inoculates several mice, one at a time, with a disease germ until he finds 3 mice that have attacked by the disease. If the probability of getting attack of the disease is 1/5, what is the probability that 10 mice are required

A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 30 minutes and a variance of 25 minutes (squared).

Required:

a) What is the probability that a randomly selected parcel will take longer than 33 minutes to deliver?

b) What is the probability that a randomly selected parcel will take less than 26 minutes to deliver?

c) What is the minimum delivery time (minutes) for the 2.5% of parcels with the longest time to

deliver?

d) What is the maximum delivery time (minutes) for the 10% of the parcels with the shortest time to deliver?

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?

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?

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?

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?

the probability of winning is 1/3. Mona plays 6 games. Find probability of winning exactly 5 games.

if you were to flip a coin 20 times what is the probability you wpuld get exactly 10 heads

IQs are designed to be N(100,225).

a. To join Mensa an IQ of 138 is required. What percentage of the population are

eligible to join?

b. A psychologist claims that any child with an IQ of 150+ is ‘gifted’. How many ‘gifted’ children would you expect to find in a school of 1800 pupils?