Statistics and Probability Answers

A new vaccine is able to give protection to 85% of bacterial disease. a. If 10 people are given the vaccines, find the probability that at least six people will be protected from the bacterial disease. 2 marks b. If 100 people are given the vaccines, find the value of n such that the probability that at least n people will be protected from the bacterial disease is 0.94. 4 marks c. State the type of distribution use to solve question (a) and (b). Briefly explain why you choose the distribution.

The average outstanding balance of loan issued by a bank varies from month to month. From past experience it is known that the amounts are normally distributed with a standard deviation of Rs. 5000. The bank wishes to estimate the average by drawing a random sample such that the probability is 0.95 that the mean of the sample will not deviate by more than Rs. 600 from the universe mean. What should be the sample size?

A research worker wishes to estimate the mean of a population by using sufficiently large sample. The probability is 0.95 that the sample mean will not differ from the true mean by more that 25% of the standard deviation. How large sample should be taken?

A manufacturing concern wants to estimate the average amount of purchase of its product in a month by the customers. If the standard deviation is Rs. 10, find the sample size, if the maximum error is not be exceed Rs. 3 with probability of 0.99.

A factory producing 50,000 pairs of shoes daily. From a sample of 500 pairs 2% were found to be substandard quality. Estimate the number of pairs that can be reasonably expected to be spoiled in the daily production and assign limits at 95% level of confidence.

Chinovac Labs tried a new vaccine on 312 randomly selected individuals. From the experiment, it was determined that 128 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the upper bound of this interval?

A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 19 months, what size sample should be taken so that at 95% confidence, the margin of error will be 4 months or less?

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 798 hours and a standard deviation of 81 hours. Find the probability that a random samples of 47 bulbs will have an average life of greater than 826 hours

A box contains 5 balls. Two are numbered 3, one is numbered 4, and two are numbered 5. The balls are mixed and one is selected 

A box contains 5 balls. Two are numbered 3, one is numbered 4, and two are numbered 5. The balls are mixed and one is selected 

at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, 

at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, 

find the mean of the numbers on the balls.

Using continuity correction probability of observing less than 10 successes answer?