A Tasmanian distillery has imported a new machine that is used to fill bottles of whisky....

A Tasmanian distillery has imported a new machine that is used to fill bottles of whisky. However, the machine cannot fill exactly the same amount of whisky into every bottle. After one month, it is observed that the quantity poured into a 1 litre bottle is normally distributed with a mean of 1.02 litres and a standard deviation of 0.1 litres.

Question 1 : What is the probability of a bottle of whisky containing less than 0.95 litres?

Question 2 : Suppose the new machine can be adjusted to any mean while leaving the standard deviation unchanged. To what mean should we set the machine so that only 1% of bottles contain less than 1 litre?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A machine is used to fill Apple Juice bottles with juice. The machine has a known...

A machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of ? = 0.05 liters. The target mean fill volume is ? = 2.0 liters. A quality control manager obtains a random sample of 50 bottles. He will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1. What is the probability that the quality control manager will shut down the machine.?

A machine used for filling plastic bottles with a soft drink has a target mean fill...

A machine used for filling plastic bottles with a soft drink has a target mean fill volume of 2.9 liters and a known standard deviation of 0.05 liter. State the sampling distribution of the sample mean, if you obtain a random sample of 25 bottles. Options- X bar ~ N(2.9, 0.01) X ~ N(2.9, 0.01) X ~ N(2.9, 0.05)

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of...

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s^2 = 0.0153 (fluid oz)^2 . Assume that the fill volume is approximately normal. Compute a 95% upper confidence bound for the population standard deviation. Provide practical interpretation of the result.

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of...

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s2 = 0.01532 (fluid ounce). If the variance of fill volume is too large, an unacceptable proportion of bottles will be under- or overfilled. We will assume that the fill volume is approximately normally distributed. Determine the 95% upper confidence bound of the variance.

The company has two machines which are used to fill bottles with the carbonated beverage. The...

The company has two machines which are used to fill bottles with the carbonated beverage. The actual amount filled in each bottle is assumed to have a normal distribution. For Machine 1, the standard deviation is known to be s1=0.015 and for Machine 2 it is known to be s2=0.018. The quality control department wants to check if the two machines fill the same net volume on average. They randomly collect 10 bottles which were filled by Machine 1, and...

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly,...

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is 16.05 ounces with a standard deviation of .005 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the observations should occur in what interval? Round answers to four decimal places.

A bottling company uses a filling machine to fill plastic bottles with a popular cola. The...

A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean 303 ml and standard deviation is 3 ml. 1. What is the probability that an individual bottle contains less than 301.1 ml? 2. What is the probability that the sample mean contents of a sample of 10 bottles is less than 301.1 ml? 3....

Do you have bad breath? A machine is programmed to fill bottles with 1.65 liters of...

Do you have bad breath? A machine is programmed to fill bottles with 1.65 liters of mouthwash in each bottle. Scope is testing that machine for its accuracy. In a sample of 29 bottles of mouthwash, the mean and standard deviation are calculated as 1.77 liters and 0.25 liters, respectively. Use Table 2. a. Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the bottles of...

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample...

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...

Subjects