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A random sample of 25 tablets of buffered aspirin contains, on average, 325.05 mg
of aspirin per tablet, with a standard deviation of 55/10 mg. Find the 95% tolerance
limits that will contain 90% of the tablet contents for this brand of buffered aspirin.
Assume that the aspirin content is normally distributed.
1.(a)Determine the largest power of 3 that divides 126!
(b)What is the coefficient of x^18y^l5 in the expansion of (7-3y) 43?
2.A man either drives his car or takes a bus to work each day. Suppose he never takes the bus two days in a row, but if he drives to work then the next day he is just likely to drive again as he is to take the bus. At the first day, he tosses a coinand if tail comes then he takes a bus to work. Otherwise he drives to work. Findthe transition probability matrix with description.
3. (a) Eighty percent of flights depart on time. Ninety percent of flights arrive
on time. Seventy percent of flights depart on time and arrive on time.
You are meeting a flight that departed on time. What is the probability that it willarrive on time?
(b)A family has two children. What is the conditional probability that both are boysgiven that at least one of them is a boy?
The chemical of COVID 19 vaccine is non-toxic to humans. Government
regulations dictate that for any production process involving COVID 19 vaccine,
the water in the output of the process must not exceed 7950 parts per million (ppm)
of COVID 19 vaccine. For a particular process of concern, the water sample was
collected by a manufacturer ‘55’ times randomly and the sample average was 7960
ppm. It is known from historical data that the standard deviation σ is 100 ppm.
What is the probability that the sample average in this experiment would exceed the
government limit if the population mean is equal to the limit? Use the Central Limit
Theorem.
The chemical of COVID 19 vaccine is non-toxic to humans. Government
regulations dictate that for any production process involving COVID 19 vaccine,
the water in the output of the process must not exceed 7950 parts per million (ppm)
of COVID 19 vaccine. For a particular process of concern, the water sample was
collected by a manufacturer ‘55’ times randomly and the sample average was 7960
ppm. It is known from historical data that the standard deviation σ is 100 ppm.
The hospitalization period, in days, for patients following treatment for a certain
type of virus X, where X has the density function f(x) = 4/{π(x2 +1)}, 0<x <55. Find
the expected value of X. that a person is hospitalized following treatment for this
disorder.
A mathematics placement test is given to all entering freshmen at Eastern
University. n = 55, ̄x = 4, ̄y = 12, "\\sum"ni=1 xi2=232, "\\sum"ni=1 xiyi=318 .Fit a simple
linear regression model between x and y
carrot. 10% of vegetarians like cucumber. 40% of meat eaters like broccoli. 60% of meat
eaters like carrot. What is the probability that a man who likes carrot is a meat eater?
2. Tossing 2 coins together, if at least one head comes roll a die else toss again. Find the
probability distribution for the random variable X which represents the number of tail as
output.
3. What is the coefficient of xâ ¹yâ ¶ in (x-y)
4. Explain Euclidâ s Algorithm with an example?
Expert's
Brightly electrical Company has three factories (𝐴,𝐵, 𝐶) that manufacture desk lamps. A quality control management knows that 35% of lamps are produced by factory 𝐴, 35% by factory 𝐵 and the other 30% by factory 𝐶. He also knows that, generally, 1.5% of desk lamps from factory 𝐴 are defective while 1% 𝑓𝑟𝑜𝑚 𝐵 are defective and 2% from factory 𝐶 are defective.
i.What is the probability that a lamp chosen at random is defective?
ii. If a randomly selected lamp is defective, what is the probability that the lamp was manufactured in factory 𝐶?
a) How many three-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9?
b) How many are less than 500? [2]
c) How many are even? [2]
3.2 Simplify
(
Five cards are drawn from a pack of 52 well-shuffled cards. Find the probability that the 4 cards are aces AND 1 card is a king.
#340153 on Dec 2023