Probability of getting COVID-19 virus in a community is 0.03. If a sample of three persons are sequentially taken at random and person to person infection is independent then:[ denoting Y= getting virus and N= not getting] Make the sample space.       Find the probability distribution of the number of persons getting virus.     Find the probability that at-least one person will get infected by the virus.

Suppose, you are running an experiment for 1024 times where the probability of success in a single experiment is 'p'. If the variance of the number of successful experiments is 256 , find p.

The weight of goods shipped in containers of a certain size is a normally distributed random variable. It is known that 65% of the containers have a net weight above 4,98 tons, and 45% of containers net weight above 5,2 tons. Find the mean and standard deviation of the net weight containers.

Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.