### Normal Distribution and ProbabilityA normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval.#### Graphs Explanation:1. **First Graph:** - **Horizontal Axis (x):** The x-axis represents the values of the random variable x, ranging from 8 to 56. - **Shaded Area (Blue):** The portion of the graph shaded in blue represents the interval from 26 to 38. This means we are looking for the probability that x is between 26 and 38. - **Distribution Curve:** The curve is a normal distribution centered at the mean value of 32, with a standard deviation of 6. ![First Graph Diagram](first_graph.png) **Probability Calculation:** - Insert the calculated probability percentage in the box provided.2. **Second Graph:** - **Horizontal Axis (x):** Similar to the first graph, the x-axis ranges from 8 to 56. - **Shaded Area (Blue):** The shaded region represents the interval from 20 to 32. Here, we seek the probability that x is between 20 and 32. - **Distribution Curve:** Again, it's a normal distribution with mean 32 and a standard deviation of 6. ![Second Graph Diagram](second_graph.png) **Probability Calculation:** - Insert the calculated probability percentage in the box provided.---### SummaryThese graphs provide visualizations for finding the probability that a randomly selected x-value falls within specified intervals of a normal distribution. You can compute these probabilities using statistical tools or z-tables for normal distributions.

Answered: Image /qna-images/answer/74f3723a-b6a7-4ca7-b94d-cef299958661.jpg

A normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval 8 14 20 26 32 38 44 50 56 8 14 20 26 32 38 44 50 56

A normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval 8 14 20 26 32 38 44 50 56 8 14 20 26 32 38 44 50 56

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: An instructor has found that the time spent by students on a particular homework assignment follows…

Q: The amount of coffee in a can has a mean of 350g. The standard deviation is 5g. Use the normal…

A: From the graph we see that between 345 and 355 the probabilities are 0.34 and 0.34 To find the…

Q: Assume that readings on thermometers are normally distributed with a mean of 0 and a standard…

Q: Let XX represent the full height of a certain species of tree. Assume that XX has a normal…

A: We have given that X = 202.2 Mean = 216.7 And standard deviation = 6.6 We have to find out the value…

Q: A Run is a 5 kilometer race. The time taken for each runner to complete the race was recorded and…

A: A Run is a 5 kilometer race.Mean Time =28 MinutesStandard deviation =5 Minutes We have to find the…

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed…

A: Given data Mean = 259 feet Standard deviation = 37 feet

Q: Let x be the number showing on a fair six-sided die. The distribution of x has a mean of 3.5 and a…

A: Central limit theorem:For iid random variables, Xi (i = 1, 2, …, n) with mean E(Xi) = µ and standard…

Q: Assume that a randomly selected subject is given a bone density test. Those test scores are normally…

A: Obtain the probability of a bone density test score greater than –1.52. The probability of a bone…

Q: Assume that blood pressure readings are normally distributed with a mean of 125 and a standard…

A: From the provided information, Mean (µ) = 125 Standard deviation (σ) = 4.7 X~N (125, 4.7) Sample…

Q: The length of time it takes to find a parking space at 8am follows a normal distribution with a mean…

Q: An amusement park ride has a bench seat designed for two passengers in each row. In this scenario,…

Q: a. The mean number of checks written per day is (Round to three decimal places as needed.) b.…

A: From given data we have : Last year, a person wrote 129 checks. 1 year = 365 days

Q: Assume that a randomly selected subject is given a bone density test. Those test scores are normally…

Q: Assume that blood pressure readings are normally distributed with a mean of 125 and a standard…

A: Given,sample size(n)=37Mean(μ)=125Standard deviation(σ)=4.7

Q: The amount of daily sales of a candy shop in weekdays is approximately normally distributed with a…

A: Let us denote: X=the amount of daily sales of a candy shop in weekdays Given that X follows a normal…

Q: Working in the garden pulling weeds/planting flowers burns an average of 200 calories per hour. If…

A: Suppose the random variable x defines the amount of calorie burnt by working in garden pulling…

Q: A population is normally distributed with mean 15 and standard deviation 2.6. Find the probability…

Q: Find the probability that the mean height of the sample is greater than 58 inches.

A: Assume that the height of adult females in the United States is approximately normally distributed…

Q: The number of automobile accidents per week in Toronto is normally distributed with a mean of 16.3…

Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…

A: Given: mean = 0.963 grams, standard deviation = 0.312 grams. The z-score follows standard normal…

Q: A lawyer commutes daily from his home to his office. The average time for a one-way trip is 24…

Q: A population of students watch an average of 7.13 hours of TV per week with a population standard…

A: It is given that the mean is 7.13 hours and the standard deviation is 3.29 hours.

Q: Working in the garden pulling weeds/planting flowers burns an average of 200 calories per hour. If…

A: given that:- Mean, μ = 200 Standard deviation, σ = 9

Q: Assume that adults have IQ scores that are normally distributed with a mean of 104 and a standard…

A: Solution Let "X" be the IQ score of adults.

Q: Assume females have pulse rates that are normally distributed with a mean of 72 beats per minute and…

A: Given that: Mean = 72 beats S. D. = 12.5 beats Sample size (n) = 25 By using standard normal…

Q: Assume that the height of a type of tree has a normal probability distribution with a mean of 55.2…

A: Given that, Assume that the height of a type of tree has a normal probability distribution with a…

Q: The average resident of Metro City produces 770 pounds of solid waste each year, and the standard…

A: We have to find probability

Q: The amount of coffee in a can has a mean of 350g. The standard deviation is 5g. Use the normal…

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

### Normal Distribution and Probability

A normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval.

#### Graphs Explanation:

1. **First Graph:**
- **Horizontal Axis (x):** The x-axis represents the values of the random variable x, ranging from 8 to 56.
- **Shaded Area (Blue):** The portion of the graph shaded in blue represents the interval from 26 to 38. This means we are looking for the probability that x is between 26 and 38.
- **Distribution Curve:** The curve is a normal distribution centered at the mean value of 32, with a standard deviation of 6.

![First Graph Diagram](first_graph.png)

**Probability Calculation:**
- Insert the calculated probability percentage in the box provided.

2. **Second Graph:**
- **Horizontal Axis (x):** Similar to the first graph, the x-axis ranges from 8 to 56.
- **Shaded Area (Blue):** The shaded region represents the interval from 20 to 32. Here, we seek the probability that x is between 20 and 32.
- **Distribution Curve:** Again, it's a normal distribution with mean 32 and a standard deviation of 6.

![Second Graph Diagram](second_graph.png)

**Probability Calculation:**
- Insert the calculated probability percentage in the box provided.

---

### Summary
These graphs provide visualizations for finding the probability that a randomly selected x-value falls within specified intervals of a normal distribution. You can compute these probabilities using statistical tools or z-tables for normal distributions.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 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, probability and related others by exploring similar questions and additional content below.

Similar questions

Assume that readings on thermometers are normally distributed with a mean of 0 and a standard deviation of 1. A thermometer is selected at random. Find the probability that the reading is less than -2.08
Assume that the height of a type of tree has a normal probability distribution with a mean of 85.9 ft and a standard deviation of 9.4 ft. A tree of this type grows in my backyard and it stands 59.6 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 74.6 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 3 decimal places.
The probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.12. There is 35 student in the class. Each student does his/her homework independently. What is the standard deviation of X, where X is the number of students who submit the homework on time?
A normal distribution has a mean of 37 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given shaded region 13 19 25 31 37 43 49 55 61 13 19 25 31 37 43 49 55 61
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 2.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 46 customers in the first line and n₂ = 52 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.3 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = !
Suppose that an airport reports that the average time it takes for a person to get through security in 25 minutes. Assume the variable is approximately normally distributed with a standard deviation of 4.5 minutes. If 102 people were selected at random, how many would be expected to make it through security in less than 20 minutes? Approximately _________would make it through in less than 20 minutes.
average number of pounds of meat that a person consumes per year is 218pounds. Assume that the standard deviation is 26 pounds and the distribution is approximately normal. 1- Find the probability that a person selected at random consumes less than 224 pounds per year 2-1f a sample of 50 individuals is selected find the probability that the mean of the sample will be less than 224 pounds per year
Assume that adults have IQ scores that are normally distributed with a mean of95.4 and a standard deviation of 16.6. Find the probability that a randomly selected adult has an IQ greater than 118.1 The probability that a randomly selected adult from this group has an IQ greater than 118.1 is what?
The overhead reach distances off adult female are normally distributed with a mean off 200 cm and a standard deviation of 8.6 cm a.Find the probability that an individual distance is greater than 209.30 cm d.Find the probability that the mean for 20 random selected distance is greater than 198.70 cm