At the scene of a crime, the police have found a blood stain, a footprint, and some threads from a fabric. All are presumed to have been left by the person who committed the crime. After analyzing the evidence it is found that: The blood type is a type found in only 10% of the population. The footprint is a size 13 men's shoe and only 7% of the population wears that shoe size. Only 25% of the population owns clothing made from a fabric that matches the thread samples found at the scene. The police have a suspect who matches all of the criteria. He has the same blood type, the same shoe size, and owns clothing matching the threads found at the scene of the crime. While this is only circumstantial evidence, what is the probability that a random person would match all of these characteristics if the three characteristics are assumed to be independent of each other

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10