**Understanding Probability in Normal Distribution**Given a normal distribution with a mean (µ) of 104 and a standard deviation (σ) of 20, and selecting a sample size (n) of 16, we address the following questions:**a. What is the probability that X̄ (the sample mean) is less than 94?**\[ P(\bar{X} < 94) = 0.0228 \]*Note: The probability is expressed as a decimal rounded to four decimal places.***b. What is the probability that X̄ is between 94 and 94.5?**\[ P(94 < \bar{X} < 94.5) = \_\_\_\_ \]*Note: Type an integer or decimal rounded to four decimal places as required.* This exercise demonstrates how to calculate probabilities related to sample means using the properties of the normal distribution.

Answered: Image /qna-images/answer/0054c944-450e-4448-9f6c-61d07e3edcea.jpg

Given a normal distribution with u= 104 ando = 20, and given you select a sample of n= 16, complete parts (a) through (d). a. What is the probability that X is less than 94? P(X <94) = 0.0228 (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X is between 94 and 94.5? P(94

Given a normal distribution with u= 104 ando = 20, and given you select a sample of n= 16, complete parts (a) through (d). a. What is the probability that X is less than 94? P(X <94) = 0.0228 (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X is between 94 and 94.5? P(94

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

Related questions

Q: The amount of pollutants that are found in waterways near large cities is normally distributed with…

A: (a) Determine the distribution of X. The distribution of X is obtained below as follows:

Q: E. Oliver Iolqpod nadi aaol olioClto ogo 8. Choose the statement(s) which is (are) true of a normal…

A: We have to find which statements are true..

Q: 2. Use TABLEA to find the PROPORTION of observations from a STANDARD NORMAL DISTRIBUTION that…

Q: What is the proportion that lies between the z scores under the normal curve? A. 0.00 and 1.00 B.…

A: Given information- We have given the z-scores and we have to find the proportion that lies between…

Q: Round all answers to 4 decimal places where possible. Let X Be the cost for a randomly selected…

A: Given Data Population Mean,μ = 27552 Population Standard Deviation,σ = 7325 X…

Q: Each sweat shop worker at a computer factory can put together 5 computers per hour on average with a…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: Assume that females have pulse rates that are normally distributed with a mean of u = 73.0 beats per…

Q: Solve for D)

Q: The amount of pollutants that are found in waterways near large cities is normally distributed with…

A: As per Bartleby guidelines I can't answer more than three sub parts per post. Hope you understand.

Q: Which of these distributions would most flat and wide? A. T-distribution for sample of size n=5…

A: We want to which of these distributions would most flat and wide

Q: Normal Distribution. Cherry trees in a certain orchard have heights that are normally distributed…

A: Given: μ=112σ18

Q: selected college. Round all answers to 4 decimal places where possible. a. What is the distribution…

A: Given Data Population Mean,μ = 27503.0 Population Standard Deviation,σ = 6757.0

Q: The random variable X has a normal distribution with mean 80 and standard deviation 6. C. What is…

A: C. The 45th percentile for X is, PX<x=0.45PX-μσ<x-806=0.45Pz<x-806=0.45 The probability…

Q: The variance of a binomial distribution for which n = 77 and p = 0.69 is: a. 8.24 b. 32.94 c. 16.47…

A: Given : Binom. dist. having : n(no. of obser.)=77 p(prob. of success)=0.69

Q: Within any distribution of scores, the location specified by z = +1 and the location specified by z…

Q: For the normal distributions shown to the right, find the probability that an observation falls in…

Q: Please help with A B C

A: Given Information: Mean μ=9.1 Standard deviation σ=1.7 Sample size n=35

Q: The amount of coffee that people drink per day is normally distributed with a mean of 15 ounces and…

A: Note: If the question contains multiple parts only allow to do first four subparts as per the…

Q: The amount of pollutants that are found in waterways near large cities is normally distributed with…

A: [NOTE : As per the rules, only the first 3 subparts are solved.] Given that, The amount of…

Q: 6.2 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in…

Q: Private nonprofit four-year colleges charge, on average, $27,088 per year in tuition and fees. The…

A: a) Consider a random variable X that defines the cost for a randomly selected college.

Q: variable value can be transformed to a Z value. e normal distribution is discrete. mal distribution…

A: Question: Why is only one normal distribution table needed to find any probability under the normal…

Q: You want to find the probability of getting a z score less than or equal to 1.2. Which distribution…

A: The best distribution for calculating this probablity is "normal distribution". We need to look for…

Q: The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a…

A: Let "X" be the average reach distance in cm. Sketch the normal curve and shade the area to the…

Q: You are given the following information obtained from a random sample of 5 observations. Assume the…

A: 20,18,17,22,18

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

100%

**Understanding Probability in Normal Distribution**

Given a normal distribution with a mean (µ) of 104 and a standard deviation (σ) of 20, and selecting a sample size (n) of 16, we address the following questions:

**a. What is the probability that X̄ (the sample mean) is less than 94?**

\[ P(\bar{X} < 94) = 0.0228 \]

*Note: The probability is expressed as a decimal rounded to four decimal places.*

**b. What is the probability that X̄ is between 94 and 94.5?**

\[ P(94 < \bar{X} < 94.5) = \_\_\_\_ \]

*Note: Type an integer or decimal rounded to four decimal places as required.*

This exercise demonstrates how to calculate probabilities related to sample means using the properties of the normal distribution.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

8. For a normal distribution with u = 500 and o = 100, find the following values: a. What X value separates the highest 10% of the distribution from the rest of the scores? b. What X values form the boundaries for the middle 60% of the distribution? %3D c. What is the probability of randomly selecting a score greater than X = 475?
need help!
d) For a standard normal distribution, find the probability a score is lower than 2.37 standard deviations above the mean? e) For a standard normal distribution, find the probability a score is between the mean and 2.37 standard deviations above the mean?
Title A random sample of 36 observations has been drawn from a normal distribution... Description </o:p> A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<></53.>
← The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 218.90 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 203.30 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four decimal places as needed.) F7 View an example Get more help - 7 F8 U F9 * 8 S 4 T DELL F10 -!!!/ ( 9 O F11 ) O F12 P Clear all PrtScr 13 { [ + 11 = Check answer 86°F Mostly sunny Insert Delete Backspace 1 2 S Inco P Ca PgUp Num Lock
J 1
2 part for uniform distr.