Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. It is known that 83% of all the orders it receives from its customers are delivered on time. Let be the proportion of orders in a random sample of 100 that are hat p delivered on time. Find the probability that the value of be less than 0.86

Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was u = 9.3 mg/L with 95% of the data ranging from 6.7 mg/L to 11.9 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. In USE SALT (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed…

The time it takes to complete an online survey is uniformly distributed over the range of 10.1 minutes to 16 minutes. Calculate the probability that it takes a person between 11.2 and 11.9 minutes to complete the survey.

A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Y1 = 0, if the policy holder does not have any health issues; Y1 = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).