A small dairy plant packages milk into 1 litre cartons. The company uses an automatedmachine for filling the milk into the cartons. From past records it is known that 1 in 8cartons that go through this machine are filled with less than 750 millilitres of milk. Arandom sample of 12 cartons that have gone through the machine is selected.1.1. State the precise random variable required to solve this problem using Binomialdistribution.1.2. State 2 of the conditions necessary for a random variable to be modelled using abinomial distribution.11.3. Find the probability that exactly two cartons are filled with less than 750 millilitres ofmilk.1.4. Find the probability that none of cartons are filled with less than 750 millilitres ofmilk.1.5. The machine will be recalibrated only if more than 3 cartons in the sample have lessthan 750 millilitres of milk.Find the probability that the machine will not need recalibration.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An exponential random variable X has a true mean value of 5. Suppose we observe n =17 independent realizations of this random variable, x1, x2,..., n. What is the variance of the sample mean?
2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:
MN.27.
The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 9. Find the standard deviation for the binomial random variable X, the number of seeds germinating in each batch Round to three decimals A. 1.375. OB. 1.296 O C. 1.281 OD. 1.358
3.37 In 2003, the average combined SAT score (math and verbal) for college-bound students in the United States was 1026. Suppose that approximately 45% of all high school graduates took this test and that 100 high school graduates are randomly selected from among all high school grads in the United States. Which of the following random variables has a distribution that can be approximated by a binomial distribution? Whenever possible, give the values for n and p. a The number of students who took the SAT b The scores of the 100 students in the sample c The number of students in the sample who scored above average on the SAT d The amount of time required by each student to complete the SAT e The number of female high school grads in the sample
The general philosophy of standardizing is that standardizing a random variable involves a. Subtracting the main in the batting by the standard deviation b. Dividing the standard deviation of the total of successes by the total of trials c. Adding and subtracting standard deviations in each direction d. Subtracting the area in the right tail from 1 since the Z chart gives only the area "to the left"
For normally distributed random variables, how would one verify the empirical rule percentages using z scores? Multiple choice question. Find P(-2 ≤ Z ≤ 2) from a standard normal table and compare to 68%. Find P(-1 ≤ Z ≤ 1) from a standard normal table and compare to 95%. Find P(-2 ≤ Z ≤ 2) from a standard normal table and compare to 99.7%. Find P(-1 ≤ Z ≤ 1) from a standard normal table and compare to 68%.
the number of tickets purchased by an indivisual for beckham colleges holiday music festival is a uniformly distributed random variable ranging from 7 to 14. find the mean and standard deviation and round to the 2 decimal places.
Suppose the horses in a large stable have a mean weight of 818 lbs, and a variance of 3481. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 18 lbs if 34 horses are sampled at random from the stable? 0.920 0.925 0.912 O 0.945 None of these t
Two normally distributed populations with H4 =µ, and both variances being 100 are given. Random samples of size 25 are taken from each population with respective sample means 104 and 100. What is the probability of observing a difference of at least 4 units between the first and second sample means? Select one: O a.None b.0.1271 c.0.8729 d.0.9207 e.0.0793

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