**Problem Statement:**Let \( x \) be a continuous random variable that has a normal distribution with \( \mu = 48 \) and \( \sigma = 8 \). Assuming \( \frac{n}{N} \leq 0.05 \), find the probability that the sample mean, \( \bar{x} \), for a random sample of 16 taken from this population will be more than 44.90.Round your answer to four decimal places.\[ P(\bar{x} > 44.90) = \] [Input Box]---**Explanation:**1. **Parameters Given:** - Population Mean (\( \mu \)): 48 - Population Standard Deviation (\( \sigma \)): 8 - Sample Size (\( n \)): 16 - Sample Mean (\( \bar{x} \)): 44.90 - Finite Population Correction Factor (Assuming \( \frac{n}{N} \leq 0.05 \))2. **Goal:** - To determine the probability that the sample mean \( \bar{x} \) for a random sample of 16 is greater than 44.90.3. **Steps to Follow:** - Calculate the standard error of the mean (SEM), which will be \( \frac{\sigma}{\sqrt{n}} \). - Convert the sample mean to a z-score using \( Z = \frac{\bar{x} - \mu}{SEM} \). - Use the z-score to find the corresponding probability from the standard normal distribution.4. **Notes:** - Round the final answer to four decimal places.

The mean and standard deviation are 48 and 8, respectively.

Answered: et x be a continuous random variable…

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

Time left 0:08:09 On average, a milk packaging machine fills milk into 1000 milliliter-packages. Sometimes, the machine makes errors with an estimated variance of 400. What is the z-score for a randomly selected milk package that measured 910 milliliters? [Give your answer correct to 1 decimal place] Answer: Next page
The distribution of certain test scores is a nonstandard normal distribution with a mean of 80 and a standard deviation of 9. What are the values of the mean and a standard deviation after all test scores have been standardized by converting them to z-scores using z=(x-µ)/σ? A) The mean is 100 and the standard deviation is 10 B) The mean is 0 and the standard deviation is 1 C) The mean is 1 and the standard deviation is 0 D) The mean is 10 and the standard deviation is 100
After visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin submarine back to the surface of the water. They start 1900 meters below the surface of the water, and ascend at 62 meters per hour.Note: under the water is a negative number.Write an equation to model this situation (use mm for meters and hh for hours)
normal distribution has mean = 38 and sd= 4 (a) Find the z score corresponding to x = 28 (b) Find the z score corresponding to x = 45.
normal distribution has mean= 250 and sd = 20. (a) Find the z score corresponding to x = 235. (b) Find the z score corresponding to x = 320.
please answer all questions fully and show all work down to the numerical values for each part
Can you please check my work
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.6 and standard deviation ? = 0.4. (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) (b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) (c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.)
please list z score an the intervals like mean and standard devation. test stastic fortmula with values the procedure name the parameter in c level context and if its random or normal
nts The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.7 grams per mile and standard deviation 0.17 grams per mile. (a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile? Hint You already have an equation that gives a relationship between the population standard deviation, the sampling distribution's standard deviation, and the sample size. Do a little algebra to solve that equation for the sample size. ANSWER: (b) If a larger sample is considered, the standard deviation for æ would be (NOTE: Enter "SMALLER","LARGER" or "THE SAME without the quotes.)
The processing time for the robogate has a normal distribution with mean 23 sec and standard deviation 2sec. Find the probability that the next operation of the robogate will take 27.4 sec or less. The probability is.
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean u - 5.3 and standard deviation a - 0.7. The Standard Normal Distribution u = 0, o = 1) -1 68% of area 95% of area 99.7% of area (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) (b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) z< (c) Convert the x interval, 4.0 < x< 5.5, to a z interval. (Round your answers to two decimal places.)

SEE MORE QUESTIONS

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

et x be a continuous random variable that has a normal distribution with μ = 48 and robability that the sample mean, x, for a random sample of 16 taken from this populat Round your answer to four decimal places. (x > 44.90) = i