Question

1. The shape of the distribution of the time required to get an oil change at a 10-minute oil change store is unknown. However, records indicate that the mean time to get an oil change at the store is 14 minutes with standard deviation of 3.2 minutes

1. To compute probabilities regarding the sample mean using the normal distribution, what sample size is required?
2. What is the probability that a random sample of 40 oil changes results in a sample mean time of less than 10 minutes?
3. Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain time goal. On a typical Saturday the oil change facility will perform 40 oil changes between 10 am and 12 pm. Treating this as a random sample, what mean oil change time would there be a 10% chance of being at that time or below?

2. A machine is used for filling plastic bottles with a soft drink. The machine is known to have a target means of 2.0 liters and a standard deviation of 0.05 liter.

1. Suppose you choose a bottle at random filled by this drink dispenser. What is the probability that volume of your bottle has less than 1.98 liters?
2. Suppose you choose 45 bottles at random filled by this dispenser. What is the probability that the mean amount in this sample is less than 1.98 liters?
3. A quality control manager obtains a random sample of 45 bottles. He will shut down the machine if the sample mean of these 45 values is less than 1.98 liters or above 2.02 liters. What is the probability that the quality control manager will shut down the machine even though the machine is correctly calibrated?

Answer 1

Let random variable X denote the time required to get an oil change at a 10 minute oil change