The shape of the distribution of the time required to get an oil change at a 20-minute oil-change facility is skewed right. However, records indicate that the mean time is 21.3 minutes, and the standard deviation is 3.6 minutes. Complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would b required? OA. The normal model cannot be used if the shape of the distribution is skewed right. OB. The sample size needs to be less than equal to 30. OC. Any sample size could be used. OD. The sample size needs to be greater than or equal to 30. (b) What is the probability that a random sample of n = 40 oil changes results in a sample mean time less than 20 minutes? The probability is approximately (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager. minutes. There is a 10% chance of being at or below a mean oil-change time of (Round to one decimal place as needed.)

From long-term observation, it is known that the waiting-time for non-ambulance adult arrivals in a hospital's A&E has a mean of 120 minutes and a standard deviation of 50 minutes. On a given day, there are 200 such arrivals. Management want to set a daily target for the mean waiting time that will be met 95% of the time with 200 arrivals. What mean should they specify? O 202.24 minutes O 124.53 minutes O 126.93 minutes O 125.82 minutes

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo.  Wood from several excavations gave a mean of (year) 1255 with a standard deviation of 40 years.  The distribution of dates was more or less mound-shaped and symmetric about the mean.  Use the empirical rule to estimate the following.   A.  A range of years centered about the mean in which about 68% of the data ( tree-ring dates) will be found between______ and ____ A. D> B.  A range of years centered about the mean in which about 95% of the data ( tree-ring dates) will be found between ______ and _____ A.D. C. A range of years centered about the mean in which almost all the data ( tree-ring dates) will be found between ______ and _____ A.D.

(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are  z3 ≈ −1.101, z4 ≈ −0.944, z9 ≈ −0.157, z14 ≈ 0.629, and z20 ≈ 1.573.  Find the mean and the standard deviation of these z-scores. mean       standard deviation   (b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a standard deviation of 8.226. The z-scores for each of the six data values are  z2 ≈ −1.459, z6 ≈ −0.973, z12 ≈ −0.243, z17 ≈ 0.365, z22 ≈ 0.973, and z25 ≈ 1.337.  Find the mean and the standard deviation of these z-scores. mean       standard deviation       (c) Use the results of part (a) and part (b) to make a conjecture about the mean and standard deviation of the z-scores for any set of data. The mean of the z-scores is always 1, and their standard deviation is 0. The mean of the z-scores is always 1 more than the standard deviation.     The mean and standard deviation of z-scores are never the same.…