Reference no: EM132848276

1) Melina recorded the number of passengers in each car of the first 100 cars that passed in front of her house on Sunday morning. The outcomes are shown in the table below:

Number of Passengers 1 2 3 4 5

Number of Cars 44 30 15 4 7

a) Find the mode and median value?

b) Find the mean value?

c) Find the standard deviation ? (Give your answer in two decimal places).

d) What is the probability a car to contain:

i) exactly 3 passengers?

ii) at least 2 passengers?

iii) at most 4 passengers?

iv) exactly 6 passengers?

v) What kind of probability is the above problem? Justify your answer.

2) Life insurance salesman meets his prospective customers separately. At each meeting, he makes the same effort to persuade the prospective client to be insured. The vendor's understanding after a long term in the insurance business is that the probability of persuading the customer to be insured (probability of success) is 0,1. What is the probability in 4 trials to insure one of them?

3) Suppose the annual savings (in millions of euros) of a specific household is a random variable, which follows the normal distribution with mean and standard deviation . If we take a random sample of 16 households from the population, what is the probability the sampling mean to be:

i) more than 5.5 million euros?

ii) between 4.9 and 5.1 million euros?

4) The strength limit of a specific type of a cable is random variable with mean value of 1500 kg and standard deviation 175 kg. The factory that manufactures this type of cables claims that they improved the materials that they used and the new resistance limit of the cable has increased. We randomly chose a sample of 50 cables and the mean strength limit was 1570 kg. If the strength limit in the specific type of cable is normally distributed with a significance level of 0.05, can we state that the claim of the manufacture factory is true? Justify your answer.