### Understanding Normal Distribution and ProbabilityA population of values has a normal distribution with the following parameters:- Mean (μ) = 23.8- Standard deviation (σ) = 91.4You intend to draw a random sample of size $ n = 150 $. Please show your answers as numbers accurate to four decimal places.#### Tasks:1. **Determine the Probability for a Single Value** Find the probability that a single randomly selected value (X) falls between 34.2 and 42.5. $ P(34.2 < X < 42.5) = \_\_\_\_\_\_ $2. **Determine the Probability for a Sample Mean** Find the probability that a sample of size $ n = 150 $ is randomly selected and has a mean ($ \bar{x} $) between 34.2 and 42.5. $ P(34.2 < \bar{x} < 42.5) = \_\_\_\_\_\_ $*Note: Click "Next Question" to proceed with the assessment.*---This example focuses on utilizing the properties of a normal distribution to calculate probabilities for both individual values and sample means. Understanding these concepts is crucial for statistical inference and practical data analysis.

The mean is 23.8 and the standard deviation is 91.4.

Answered: A population of values has a normal…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A sample of size 126 will be drawn from a population with mean 26 and standard deviation 3. Use the TI-84 calculator. Part 1 of 2 Find the probability that x will be between 25 and 27. Round the answer to four decimal places. The probability that x will be between 25 and 27 is Part 2 of 2 th Find the 55 percentile of X. Round the answer to two decimal places. The 55th percentile is
A population of values has a normal distribution with 45.2 and a 67.7. You intend to draw a random sample of size n = 108. Please answer the following questions, and show your answers to 1 decimal place. Find the value separating the bottom 35% values from the top 65% values. Find the sample mean separating the bottpm 35% sample means from the top 65% sample means.
The number of ants per acre in the forest is normally distributed with mean 45,000 and standard deviation 12,005. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. please answer all 3 subs B, C, and D round all answers to 4 decimal place where possible thank youb. Find the probability that a randomly selected acre in the forest has fewer than 54,589 ants. c. Find the probability that a randomly selected acre has between 48,168 and 56,283 ants. d. Find the first quartile. ants (round your answer to a whole number)
A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces. What is the probability of filling a cup between 25 and 31 ounces? Round your answer to four decimal places. Answer esc If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. angle. 9 ! 1 9 a Z ← @ 2 W S X # 3 e d C C $ 4 r f % 5 V t Oll A 6 Normal Table - to-z Normal Table - to z b y h & 7 n O u * 8 3 O i N ( 9 k O < 1 alt ) 0 1 Р O - : Tables ; Submit Answer 4 ? 1 + = Keypad Keyboard Shortcuts 31 11 1 Oct 28 }. backspace 1 USE YOUR SMARTPHONE FOR 2:53 3 D45 enter
pls help me and write the solution down on a paper if you can thank you
Suppose the masses of a batch of 2000 potatoes have a mean of 60 grams with a standard deviation of 8 grams. Assuming the weights have a normal distribution, predict the number of potatoes that would have masses between 45 and 55 grams. Sketch the distribution curve, shade the required probability, and show horizontal scales the population parameters and the z-scores. Solve the problem
The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7.1 mm. Suppose that 46 individuals are randomly chosen. Round all answers to 4 where possible. Question for the group of 46, find the probability that the average length is more than 188.
A population of values has a mean of 38.5 and standard deviation of 80.4. Find the probability that a sample of 247 values from this population will have a mean between 31.3 and 44.1.
This is a normal distribution problem The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2927 and standard deviation 654. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.
If we meet these conditions, the sampling distribution of the mean will have a normal shape and ... The mean of the sampling distribution will be u, (i.e., the same as the population mean) and the standard deviation of the sampling distribution will be (that's the population standard deviation divided by the square root of the sample size). In the AP Stats Guy video, he talks about the number of text messages his students send during class. Suppose the average number of text messages his students send during class is u = 30 text messages. If we take samples of say, n = 36 students at a time, we would expect the mean of the sampling distribution we create to be the same as the population mean, 30 text messages. If we can further say that standard deviation of the number of text messages is 12 text messages, by how much would we expect the sample means to vary? (hint, use the formula above) text messages

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS