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 µ=303 ml and standard deviation σ= 5 ml
a)
Given,
= 303 , = 5
We convert this to standard normal as
P(X < x) = P(Z < ( x - ) / )
So,
P(X > 305) = P(Z > ( 305 - 303) / 5)
= P(Z > 0.4)
= 0.3446
b)
Using central limit theorem,
P( < x) = P(Z < ( x - ) / / sqrt(n) ) )
So,
P( < 302) = P(Z < ( 302. - 303 ) / (5 / sqrt(100) ))
= P(Z < -2)
= 0.0228
A bottling company uses a filling machine to fill plastic bottles with a popular cola. The...
Terms 2 Questions 3 Scores on the Stanford-Rinst i test are assumed to be normally standard deviation of 15 10% of the population? testare assumed to be normally distributed with a mean of 100 and a wit percent of the portation score above 1257 Below what score lie the lowest l Question 4. A task consists of installing an electric harness under the dashboard of a General Motors car. Assume that the times for these tasks are normally distributed with...
1. The heights of kindergarten children are approximately normally distributed with a mean height of 39 inches and a standard deviation of 2 inches. A classroom of 20 of these children is used as a sample. What is the probability that the average height , for the class is greater than 40 inches? Illustrate with a graph. ANSWER: 0.0127 2. The heights of kindergarten children are approximately normally distributed with a mean height of 39 inches and a standard deviation...
A soft drink company produces bottles of cola that are supposed to contain 10 ounces. When the bottling machine is working correctly, the number of fluid ounces per bottle is in fact normally distributed with mean 10 ounces and standard deviation 0.42 ounces. A customer buys nine bottles of this type of cola. What is the probability that the average volume of cola in the nine bottles is more than 9.7 ounces but less than 10.2 ounces? (A) 0.9074 (B)...
12. The Crown Bottling Company has installed a new bottling process that will fill 12-ounce bottles of Cola. Both overfilling and underfilling of bottles is undesirable. The company wishes to see whether the mean bottle fill, μ, is equal to the target of 12 ounces. The company samples 43 bottles. The sample mean is 11.91 and the standard deviation is such that σ=0.11. a) Use a hypothesis test, at a 1% level of significance to determine whether the filler should...
The Crown Bottling Company has just installed a new bottling process that will fill 11-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, u, is close to the target fill of 11 ounces. To this end, a random sample...
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...
Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is normally distributed with mean 12.01 oz and standard deviation 0.2 oz (a) What is the probability that a randomly selected bottle contains a volume less than 12 oz? [Select ] (b) What is the probability that the mean volume of a random sample of 49 bottles is less than 12 oz? 0.3632 OZ
An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approximately normal with a mean of 1.0 liter and a standard deviation of 0.02 liters. Output mean is monitored daily by using 100 samples, each with 25 observations. Determine three sigma upper and lower control limits. Select one: a. UCL = 1.012; LCL = 0.988 О b. UCL = 1.006; LCL = 0.994 O c. UCL = 1.02; LCL = 0.98 d. none of...
Problem 2. An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approxi- mately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. a. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. b. Given these sample means: 1.005, 1.001,.998, 1.002, 995, and.999, is the process...
the example for 5.31 is also attached 5.33 Can volumes. Averages are less variable than individual observations. It is reasonable to assume that the can volumes in Exercise 5.31 vary according toa Normal distribution. In that case, the mean x of an SRS of cans also has a Normal distribution (a) Make a sketch of the Normal curve for a single can. Add the Normal curve for the mean of an SRS of five cans on the same sketch. (b)...