Given that x is a normal variable with mean u = 44 and standard deviation o = 6.3, find the following probabilities. (Round your answers to four decimal places.) (a) P(x < 60) (b) P(x 2 50) (c) P(50 s xS 60)

TF.5 A small hotel has 5 rooms. Let X be the number of occupied rooms on any given day. The pmf p(x) of X is given in the table. x 0 1 2 3 4 5 p(x) .05 .05 .20 .25 .30 .15 Find the means E(X) and E(X2) , the variance V(X) and the standard deviation SD(X) of X.

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 0.6 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 31, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit. a. At what value should the control limit be set? (Round z values to two decimal places. Round your answers to 2 decimal places.) b. If the population mean shifts to 8.7, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.) c. If the population mean shifts to 9.4, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)