The heat evolved in calories per gram of a cement mixture is approximately normally distributed. the mean is thought to be 101.1 and the standard deviation is 5.8. we wish to test upper h subscript 0 baseline colon mu equals 101.1 versus upper h subscript 1 baseline colon mu not-equals 101.1 with a sample of n=9specimens.
(a) if the acceptance region is defined as 98< xbar< 102, find the type 1 error probability α.
(b) find β for the case where the true mean heat evolvedis 103.
(c) find β for the case where the true mean heat evolvedis 105. this value of β is smaller than the one found in part(b) above. why?

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. a vending machine will only accept coins weighing between 5.48 g and 5.82 g. what percentage of legal quarters will be rejected? round your answer to two decimal places.

In the diagram, points d and e are marked by drawing arcs of equal size centered at b such that the arcs intersect ba and bc. then, intersecting arcs of equal size are drawn centered at points d and e. point p is located at the intersection of these arcs. based on this construction, m , and m