Essay Standard Deviation – Mode Value – Mathematics Assignment Help

Assignment Task:

1). The 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 of 4 trials to ensure one of them? 

2). Suppose the annual savings (in millions of euros) of a specific household is a random variable, which follows the normal distribution with mean μ=5 and standard deviation σ=1. If we take a random sample of 16 households from the population, what is the probability the sampling mean to be:

1. more than 5.5 million euros? 
2. between 4.9 and 5.1 million euros?

3). The strength limit of a specific type of cable is a random variable with a mean value of 1500 kg and a standard deviation of 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.