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 6 minutes and the standard deviation is 3 1 minutes a To compute probabilities regarding the sample mean using the normal model what size sample would be required The sample size needs to be greater than 30 The normal model cannot be used if the shape of the distribution is unknown The sample size needs to be less than 30 Any sample size could be used b The probability that a random sample of n 42 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 andom sample at what mean oil change time would there be a 9 chance of being at or below This will e the goal established by the manager here would be a 9 chance of being at or below minutes Round to the nearest 1