The diameters of apples grown in an orchard are normally distributed with mean3.4 and standard deviation 0.4 inches.(a) What proportion of the apples have diameters greater than 4.0 inches? Whatproportion have diameters less than 3.0 inches?(b) If two apples are selected at random, what is the probability that thedifference in their diameters exceeds 0.5 inches?(c) If four apples are selected at random, what is the probability that theiraverage diameter exceeds 4.0 inches?(d) If ten apples are selected at random, what is the probability that exactly twohave diameters less than 3 inches and exactly one has diameter greater than 4inches?

Mean μ=3.4 Standard deviation σ=0.4

Answered: The diameters of apples grown in an…

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

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 57 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 57 tons and standard deviation ? = 1.2 ton. (a) What is the probability that one car chosen at random will have less than 56.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 39 cars chosen at random will have a mean load weight x of less than 56.5 tons of coal? (Round your answer to four decimal places.)
The size of fish is important to commercial fishing. A study conducted in 2102 found that the length of Atlantic cod caught in nets in Karlskrona, Sweden is normally distributed with mean 47 cm and standard deviation 3.4 cm. 1.What is the probability that a randomly Atlantic cod is between 44 and 49 cm? Round your answer to 4 decimal places. 2.What is the probability that a random sample of 5 Atlantic cod have an average length between 44 and 49 cm? Enter your answer rounded to 4 decimal places. Document how you obtained your answer in the space provided below. 3.Why did the probability increase?
The mean GPA for students in School A is 3.0; the mean GPA for students in School B is 2.8. The standard deviation in both schools is 0.25. The GPAs of both schools are normally distributed. If 9 students are randomly sampled from each school, what is the probability that: (a) the sample mean for School A will exceed that of School B by 0.5 or more? (b) the sample mean for School B will be greater than the sample mean for School A?
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 40 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (c) What is the probability that the sample mean is within 1 inch of the population mean for New York?.
Lloyd's Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 25 boxes is selected at random from the production line every hour, and if the average weight is less than 15 ounces, the machine is adjusted to increase the amount of cereal dispensed. If the mean for 1 hour is 1 pound and the standard deviation is 0.1 pound, what is the probability that the amount dispensed per box will have to be increased? a) 0.0018 b) 0.2009 c) 0.0009 d) 0.9991 e) 0.2660 f) None of the above
The mean annual salary for nurses is $65,000 with a standard deviation of $7,000. What is he probability that a randomly selected nurse has a salary less than $60,000? A random sample of 50 nurses is selected. What is the probability that the sample mean annual salary is less than $60,000?
A machine produces small rods and large rods. The diameters of small rods are normally distributed with mean 2 cm and standard deviation 0.12 cm. The diameters of large rods are normally distributed with mean 2.2 cm and standard deviation 0.15 cm. (i) Find the probability that a randomly chosen small rod has diameter greater than 2.15 cm. (ii) A box contains one small rod and one large rod. Find the probability that at least one of the rods has diameter greater than 2.15 cm.
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 69 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 69 tons and standard deviation ? = 1.5 ton. (a) What is the probability that one car chosen at random will have less than 68.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 46 cars chosen at random will have a mean load weight x of less than 68.5 tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than 68.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? YesNo Suppose the weight of coal in 46 cars selected at random had an average x of less than 68.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this…
A manufacturer knows that their items have a normally distributed length, with a mean of 5.7 inches, and standard deviation of 1 inches.If one item is chosen at random, what is the probability that it is less than 6 inches long?
A manufacturer knows that their items have a normally distributed length, with a mean of 10 inches, and standard deviation of 3.2 inches.If 3 items are chosen at random, what is the probability that their mean length is less than 12.2 inches?
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 54 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 54 tons and standard deviation ? = 1.4 ton. (a) What is the probability that one car chosen at random will have less than 53.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 26 cars chosen at random will have a mean load weight x of less than 53.5 tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than 53.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? YesNo Suppose the weight of coal in 26 cars selected at random had an average x of less than 53.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this deviation…

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