The amount of water in a bottle is approximately normally distributed with a mean of 2.50 liters with a standard deviation of 0.025 liter. Complete parts (a) through (e) below. a. What is the probability that an individual bottle contains less than 2.48 liters? 0.212 (Round to three decimal places as needed.) b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.48 liters? 0.055 (Round to three decimal places as needed.) c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.48 liters? 0.000 (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bottle, which can be thought of as a sample with sample size 2.48|. Therefore, the standard error of the mean for an individual bottle is 0 times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is larger than the probability in part (c). (Type integers or decimals. Do not round.) e. Explain the difference in the results of (b) and (c). The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is greater than in (b). As the standard error decreases, values become more concentrated ound the mean. Therefore, the probability that the sample mean will fall close the population mean will always increase when the sample size increases.

Q: Siding Alyrnials -30x 2. box +12 X

A: Let's find.

Q: How many faces, edges and vertices does the following figure have? Faces = Edges %3D Vertices =

A: Solving

Q: 3. 80 km/h Two cars meet at an intersection. One travels north at an average speed of 80 km/h. The…

A: Let, the intersection point be denoted by O(origin) .  The first car travels to the north at an…

Q: Find class boundaries, midpoint, and width for the class. 40-54 Part: 0/3 Part 1 of 3 The class…

A:

Q: y! Netflix - AVG X Movies - Net Watch Free y Amazon Prin x Prime Video: X y! prairie view a X 6.3…

A: The objective of this question is to calculate the total monthly payment that Oliver needs to make…

Q: (e) The table gives the amount of carbon emitted into the atmosphere in carbon dioxide from 1860 to…

A:

Q: A test consists of 10 true/false questions. To pass the test a student must answer at least 8…

A: Hey there! Thanks for posting the question. However, we can answer only first three sub-part…

Q: What is the distance SR? S -70 -22 O-48 units O -92 units O 92 units O 48 units

A: The solution of given problem is followed by

Q: (sin" (e* 3 + cos I -00

A: We first get rid of the negative exponents

Q: R A II II II Horse Race Alababa, Bubba, Cory, and Dandy are in a horse race. Bubba is the slowest;…

A: Topic = Algebra

Q: Explain the concept of Degrees of Freedom through an example:

A:

Q: Time series plots – Analyze each of these cycle time data separately: C3, C12, C13. That means three…

A: Given data, C3 C12 C13 19.98 29.95 20.48 20.01 30 20.2 20.02 30…

Q: Please help me ? Doing research on the mathematics involved in a medical topic . To help you…

A: In medical field, one of the most commonly dealt issue is deciding the dosage of a certain medicine…

Q: A company prouces candles in a wide variety of colors and style. A customer requires 25,000 candles…

A: 1 candle time = Total TimeTotal Candle

Q: A bus holds 40 students if the school fills three one and a half buses for a field trip how many…

A:

Q: One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a…

A: Given Information: One common system for computing a grade point average assigns 4 points to an A. 3…

Q: Roll a fair die repeatedly; X� represents the number of rolls it takes to get a six.

A: Roll a fair die repeatedly; X represents the number of rolls it takes to get a six.

Q: *2. At a lumber company, shelves are sold in 4 types of wood, 3 different widths and 6 different…

A: 4 type of wood 3 different widths 6 different lengths   how many different type of shelves could be…

Q: Use the illustration to find the volume of the bowling ball and the cardboard box it is packaged in…

A: S

Q: Given a 10 gallon fish tank, a 13 gallon trash can, a 20 gallon barrel, a 2 liter bottle, a 1 cup…

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.