Statistics and Probability Answers

suppose that 9 people, chosen at random, are asked if they favour a certain proposal. find the probability that majority of the persons polled will favour proposal, given that 45 percent of the population favour the proposal

Suppose that the operations manager of a nose mask packaging delivery service is contemplating the purchase of a new fleet of trucks during this COVID-19 period. When packages are efficiently stored in the trucks in preparation for delivery, two major constraints have to be considered. The weight in pounds and volume in cubic feet for each item. Now suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard deviation of 3.9 pounds. In addition suppose that the average volume for each of these packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the variation of the weight and volume?

A survey of two new antidandruff shampoos A and B was conducted by a healthcare organization. 3/4 of the people who bought shampoo A got rid of dandruff, whereas the 7/8 of the people who used shampoo B were satisfied with the shampoo. Among the surveyed people, 3/4 of them bought shampoo A while the rest bought shampoo B. What is the probability of people getting rid of dandruff irrespective of which shampoo they used?

Traffic police checked the CNICs and driving licenses of all the people driving any vehicle on a particular road on a given day. 85% of the drivers were carrying valid CNICs and 75% of the drivers were carrying valid driving licenses. 65% of the drivers were carrying both valid CNICs and driving licenses. What percent of those who were carrying a valid CNIC were also carrying a valid driving license? What percent of those who were carrying a valid driving license were also carrying a valid CNIC?

In a university, 80% of the students are studying in various engineering disciplines and the rest are pursuing non-engineering degrees. 60% of the engineering students use IEEExplore for research and 45% of non-engineering students avail the IEEExplore service. A student is randomly selected from the university and asked whether he uses IEEExplore service or not. If the student turns out to be the user of the service, what is the probability that the randomly selected student is an engineering student? What is the probability that the randomly selected student is a non-engineering student?

Due to Covid 19, managers of mining companies are deciding to have fewer workers, the workers size in a company has decreased over the past months. According to Chamber of Mines report, the mean workers size was 3.18 in 2019. A researcher wanted to check if the current mean workers size is less than 3.18. A sample of 900 workers taken this year by this researcher produced a mean workers size of 3.16 with a standard deviation of 0.70. Using the 0.025 significance level, can you conclude that the mean workers size has decrease since 2019?

A Covid 19 testing machine at a testing centre breaks down an average of three times per year. Using an appropriate probability distribution formula, find the probability that during the next year, this machine will have;

i. exactly two breakdowns

ii. at most one breakdown