Claim that the standard deviation is at least 25. Express the null hypothesis and the alternative hypothesis in a symbolic form.

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the time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and standard deviation of 5 minutes.  What intervals could you estimate without using the Z-score table and that do not include the mean as a max or min?  For example,   is an interval we know that includes the mean as the maximum of the interval. Another example is   as an example of a probability interval that includes the mean as the minimum and 57 as the maximum. Include at least 7 intervals, their probabilities and a sketch in your answer.

A company manager plans to purchase a machine. The company requires a high quality machine. The manager is currently considering two companies that supply this machine. The machine from company A can produce approximately1050 units in average per day, but the standard deviation of this machine is about 250 units per day; while the machine from company B can produce approximately 900 units in average per day, but the standard deviation of this machine is about 100 units per day. Both of these two companies guarantee at least 10 years life. In addition, both prices are similar although machine A is a little bit higher. Price is not the main concern for the manager because both prices are under their budget. However, the manager cannot decide which machine should be purchased, because he is not sure what test he needs to conduct. Can you recommend the manager what test the manager should conduct? Should the manager conduct the test about the difference between two population means or the…