The shape of the distribution of the time required to get an oil change at a 10-minute oil- change facility is unknown. However, records indicate that the mean time is 10.5 minutes, and the standard deviation is 4 minutes. (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? O Any sample size could be used. The sample size needs to be greater than 30. O The normal model cannot be used if the shape of the distribution is unknown. O The sample size needs to be less than 30. (b) The probability that a random sample of n = 46 oil changes results in a sample mean time less than 10 minutes is approximately Round to 4 decimal places. (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 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, at what mean oil-change time would there be a 11% chance of being at or below? This will be the goal established by the manager. There would be a 11% chance of being at or below to the nearest 1 decimal place minutes. Round