A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 19.8 inches, and standard deviation of 3.3 inches. If 31 items are chosen at random, what is the probability that their mean length is greater than 18.1 inches? (Round answer to four decimal places)

A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 19.8 inches, and standard deviation of 3.3 inches. If 31 items are chosen at random, what is the probability that their mean length is greater than 18.1 inches? (Round answer to four decimal places)

Related questions

Q: A manufacturer knows that their items have a lengths that are skewed right, with a mean of 19.4…

A: Solution : Mean = 19.4 Standard deviation = 2.8 Sample size = 36 P(xbar > 18) z-statistic: (xbar…

Q: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation…

A: (a) Obtain the probability that pregnancy will last 307 days or longer. The probability that…

Q: The diameters of ball bearings are distributed normally. The mean diameter is 87 mm and the standard…

Q: The cost of textbooks is normally distributed with a mean of $223. You do not know the population…

Q: Given the mean is 120 minutes and the standard deviation is 30 minutes. What is the probability that…

A: The mean is 120 minutes and standard deviation is 30 minutes.

Q: In a survey of a group of men, the heights in the 20, 29 age group were normally distributed with a…

Q: If a male passenger is randomly selected, find the probability that he can fit through the doorway…

A: It is given that Mean, μ = 69 Standard deviation, σ = 2.8

Q: Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.7…

A: Given Data Population Mean,μ = 2.7 Population Standard Deviation,σ = 0.3 sample…

Q: The mean GPA of university students is 2.3 with a standard deviation of 1.2. If you were to draw 36…

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

A: Mean = 243 feet SD = 54 feet Find the value of z to get answers.

Q: The owner of a computer repair shop has determined that their daily revenue has mean $7200 and…

A: We have given that Mean(µ) = 7200Standard deviations (σ) = 1200 Number of days (n) = 30

Q: A quart of Parker's milk contains a mean of 39 grams of butterfat, with a standard deviation of 2…

A: Mean = 39 Standard deviation = 2

Q: High school girls average 80 text messages daily. Assume the population standard deviation is 15…

A: Given information:

Q: The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard…

Q: If 70 shafts are sampled at random from the batch, what is the probability that the mean diameter of…

A: Let X be the random variable of the diameter of metal shafts produced in a manufacturing…

Q: The mean weight of an adult is 79 kilograms with a standard deviation of 10 kilograms. If 188…

A: Let X be the random variable from normal distribution with mean (μ) = 79, standard deviation (σ) =…

Q: Suppose a batch of steel rods produced at a steel plant have a mean length of 178 millimeters, and a…

A: From the provided information,Mean (µ) = 178Standard deviation (σ) = 12Sample size (n) = 76

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

A: Let, X=the distance of fly balls hit to the outfield (in baseball) Given that X is normally…

Q: The lengths of pregnancies are normally distributed with a mean of 266days and a standard deviation…

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 lengths of pregnancies are normally distributed with a mean of 266 days and a standard…

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

Q: The weight of elephants at a zoo in Pittsburgh has a population mean of 5.3 tons and population…

A: Given Mean(μ)=5.3standard deviation(σ)=1.2sample size(n)=12

Q: a. Find the probability of a pregnancy lasting 308 days or longer. b. If the length of pregnancy is…

A: Given Data Population Mean,μ = 269 Population Standard Deviation,σ = 15

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

Q: A racing car consumes a mean of 103 gallons of gas per race with a standard deviation of 6 gallons.…

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

A: GivenMean =253Standard deviation =45 a)Let X be distribution of distance of fly balls hit to…

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

Q: The weight of rice is normally distributed. Each bag of rice weighs with a mean of 50 pounds and a…

Q: he cost of textbooks is normally distributed with a mean of $249. You do not know the population…

A: Given Information: The cost of textbooks is normally distributed with a mean of $249. Mean = 249…

Q: a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball…

A: Mean = 245s = 54

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

Q: If the probability of a defective bolt is 0.1, find he mean he standard deviation for the…

A: a) If the probability of a defective bolt is 0.1. Given that there are total of 400. That is, n=400…

Q: Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2.4…

A: Solution: Denote X as the diameter of a randomly selected metal shaft produced in the manufacturing…

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

A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 19.8 inches, and standard deviation of 3.3 inches.

If 31 items are chosen at random, what is the probability that their mean length is greater than 18.1 inches?

(Round answer to four decimal places)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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

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.