Ex 1. There are two machines available for cutting corks intended for use in winebottles. The first produces corks with diameters 3 cm. The second machineproduces corks with diameters 3.04 cm. Acceptable corks have diametersbetween 2.9 cm and 3.1 cm. The probability that the diameter of the corkproduced on the first machine will deviate from the standard by more than0.1 mm is 0.002. The probability that the diameter of the cork produced onthe second machine will deviate from the standard by more than 0.096 mmis 0.001.There are 5000 corks produced by first machine and 4000 corks are produced bythe second machine.a) Find the most probable number of defective corks among the products producedby each machine and calculate their probability.b) We randomly selects 50 corks from the first machine products and 40 corksfrom the second machine products. Find the probability that1) at most 3 corks produced on the first machine is defected2) at most 2 corks produced on the second machine is defectedc) We mix the machine product (5000 corks and 4000 corks) and then randomlyselected 10 cork. Find the probability that at most 1 corks will be defected.

General guidance Concepts and reason Normal distribution: Normal distribution is a continuous…

Answered: Ex 1. There are two machines available…

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

Similar questions

From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?
You want to find the probability that people will return a shopping cart to the corral after loading the groceries in their vehicle. For a 4 hours period, you observe the number of people who returned their cart and the number who did not. A success in this case would be that the person returned their cart. Choose the best statistical tool to calculate this probability A. Use the Central Limit Theorem to find the probability that the sample mean exceeds a certain value B. Use the empirical rule to find the number of cars that bracket 68% of the data C. Calculate a confidence interval for the population mean D. Calculate the total number of successes divided by the total number of observations to find the observed probability
A farmer only grows apple and orange trees in his orchard. 40% of his trees are apple trees. He is concerned that a parasite may be infecting his trees. The probability of the parasite infecting a given apple tree is 5% and the probability of the parasite infecting a given orange tree is 3%. Please give your answers to 3 decimal places, for example 0.305. a) What proportion of his trees are infected by the parasite? Your answer is 1 b) If a given tree is not infected, what is the probability that this tree was an apple tree? Your answer is
Assume that X has a normal distribution, and find the indicated probability. 7) The mean is μ = 15.2 and the standard deviation is o = 0.9. Find the probability that X is between 14.3 and 16.1. A) 0.1587 B) 0.6826 C) 0.8413 D) 0.3413 7)
From observations of the weather, it is known that on October 20 the probability of rain is 0.25. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?
Please solve all the questions 5. Two draws are made at random without replacement from a box with four numbers: 1, 2, 3, 4. Find the probability that the second draw will be a 3 . 6. For some positive value of X, the probability that a standard normal variable is between 0 and +2X is 0.4452. the value of X is 7. A fair die is tosses twice, and and the up face is recorded each time. Let X be the sum of the up faces. What is P(X<8) ?
Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that a SRS of size 200 would come within plus or minus 3 percentage points of this true value. In other words, find probability that ˆ p takes a value between 0.17 and 0.23.
A continuous random variable is normally distributed. The probability that a value in the distribution is less than 135 is 0.3454. Find the probability that a value in the distribution is greater than 135
The volume of blood in an adult human body follows a normal distribution with a mean of 5.2 liters and a standard deviation of 0.3 liters. Use this information to answer questions 11- 13 and remember required steps. 11. If a random sample of 16 adults is selected, calculate the probability that their mean blood volume is lower than 5.4 liters. 12. If a single adult is selected, calculate the probability the blood volume is higher than 5.9 liters. 13. What is the first quartile for blood volume for all adults?

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS