A certain pen has been designed so that true average writing writing machine) is at least 12 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, a a normal probability plot of the resulting data supports the use of a one-sample t test. 1. What hypotheses should be tested if the investigator believe a priori that the design specification has been satisfied? 2. What conclusion is appropriate if the hypotheses of part (a) are tested, t= -2.5, and a= .05? 3. What conclusion is appropriate if the hypotheses of part (a) are tested, t= -2, and a = .01? 4. What should be concluded if the hypotheses of part (a) are tested and != -3.25?

5) The daily revenue at a university snack bar has records to indicate that the mean daily revenue is $2,400 and standard deviation is $600. A random sample of 81 days was selected. Find the approximate probability that the average revenue for the sample is less than $2,300.

13) For a random variable with mean=10 and standard deviation=2, (show work) a. Find the value that corresponds to z-score=-2.4. b. applying Chebeche's Rule, find value of k such that at least 60% of the measures are within k standard deviation of the mean.

a) Turkey is the most tea-loving country in the world. In 2014, the annual per capita consumption of tea in Turkey, denoted X, was normally distributed with a mean of 6:96 lb and a standard deviation of 2:36 lb. b)You pick a random sample of 5 people from Turkey (assume all of them are tea drinkers) and compute their mean per capita tea consumption to be only 3:98 lb. (i) What is the probability that her random sample has an average of 3:98 lb or lower, when the population average is as given above? (ii)Recall that a large sample size makes it unlikely thatthe sample mean is too far away from the population mean. How big a samsle should you have to draw so that the standard deviation of your sample average is less than 10% of its mean (i.e., less than 0.696 lb)?

The proportion of items in a population that possess a specific attribute is known to be 0.25   a. If a simple random sample of size n=100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.30, what is the sampling error   b. Referring to part a, what is the probability that a sample size of 100 would have a sample proportion of 0.30 or less if the population proportion is 0.25

3. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. a). Find the probability that for 36 jets the average taxi and takeoff time is less than 8.33 minutes per plane. b). Find the probability that for 36 jets the average taxi and takeoff times is more than 8.55 minutes.