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TOPIC: Approximation of Binomial distribution using Normal and Poisson distribution.
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Additional Problem 6. Suppose that a sample of n 120 tires of the same type are obtained at rando...
1. In a particular facility, 60% of students are men and 40% are women. In a...
1. In a particular facility, 60% of students are men and 40% are women. In a random sample of 50 students what is the probability that more than half are women? Let the random variable X = number of women in the sample. Assume X has the binomial distribution with n = 50 and p = 0.4. What is the expected value and variance of the random variable X? (6 points) In a random sample of 50 students what is...
Suppose that 12% of the population of the U.S. is left-handed. If a random sample of...
Suppose that 12% of the population of the U.S. is left-handed. If a random sample of 130 people from the U.S. is chosen, approximate the probability that at most 14 are left-handed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) x 5 ?
Suppose that a simple random sample of n = 6 individuals is obtained from a population...
Suppose that a simple random sample of n = 6 individuals is obtained from a population that is skewed right with mean u = 44 and standard deviation o =2. (a) The shape of the sampling distribution of the sample mean is approximately normal. Is this true or false? (b) What is the mean of the sampling distribution of the sample mean? (c) What is the standard deviation of the sampling distribution of the sample mean? (a) Choose the correct...
6. Let X1, . . . , Xn denote a random sample (iid.) of size n...
6. Let X1, . . . , Xn denote a random sample (iid.) of size n from some distribution with unknown μ and σ2-25. Also let X-(1/ . (a) If the sample size n 64, compute the approximate probability that the sample mean X n) Σηι Xi denote the sample mean will be within 0.5 units of the unknown p. (b) If the sample size n must be chosen such that the probability is at least 0.95 that the sample...
Let x be a binomial random variable with n = 20 and p = 0.05. Calculate...
Let x be a binomial random variable with n = 20 and p = 0.05. Calculate p(0) and p(1) using Table 1 to obtain the exact binomial probability. (Round your answers to three decimal places.) p(0) = p(1) = Calculate p(0) and p(1) using the Poisson approximation. (Round your answer to three decimal places.) p(0) = p(1) = Compare your results. Is the approximation accurate? No the approximation is not accurate. At least one the differences between the probabilities from...
Select: less than, greater than or equal to Let X have อ bnon ial distribution witn parameters n-25 and ρ Calculate eac...
Select: less than, greater than or equal to
Let X have อ bnon ial distribution witn parameters n-25 and ρ Calculate each orthe following probabilities using the normal nation with the continuity correction to the cases ρ-0.5 0.6 and 0.8 and compare to the exact binomial probabilities calculated pro directly trarn the tarmula tar hn,p). (Round your answers ta tour decimal places.) (a) P(15X 20) P(15 s x s 20) P14.5 Normal 20.5) 0.S D.6 The nor nal approxim tion...
Let X have a binomial distribution with parameters n 25 and p. Calculate each of the following probabilities using...
Let X have a binomial distribution with parameters n 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p-0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x;n, P). (Round your answers to four decimal places) (a) P15 s X 20) P P(1S s Xs 20) P(14.5 S Normal s 20.5) 0.5 0.6 0.8 The normal approximation of P(15 s X...
Q.A manufacturer produces large quantities of colored mugs. It is known from previous records that 6%...
Q.A manufacturer produces large quantities of colored mugs. It is known from previous records that 6% of the production will be green. A random sample of 10 mugs was taken from the production line. 1.Define a suitable distribution to model the number of green mugs in this sample. 2.Find the probability that there were exactly 3 green mugs in the sample. 3.A random sample of 125 mugs was taken. Find the probability that there were between 10 and 13 (inclusive)...
Suppose voters from a simple random sample of 500 (N > 1,000,000) are interviewed and asked...
Suppose voters from a simple random sample of 500 (N
> 1,000,000) are interviewed and asked which presidential
candidate they're going to vote for. Of these, 35% say they'll vote
for the Statistics Party. You want to know the probability,
assuming this proportion is correct for the population, that more
than 40% of a random sample of 500 people will vote for the
Statistics Party. Which of these shows the three ways you could
find your answer?
A.
A-Using the...
: Let Yi, ½' . . . , Yn be an iid random sample from an exponential distribution with parameter where θ > 0. Here each Y, represents the lifetime of the ith battery, while θ represents the the...
: Let Yi, ½' . . . , Yn be an iid random sample from an exponential distribution with parameter where θ > 0. Here each Y, represents the lifetime of the ith battery, while θ represents the theoretical average lifetime. The pdf of each Y, is therefore given by fy (y) ei-1,2,...,n Consider the empirical average lifetime of the sample of n batteries given by Let a E R be a nonnegative real number. Consider the event A, defined...
Suppose that 12% of the population of the U.S. is left-handed. If a random sample of 130 people from the U.S. is chosen, approximate the probability that at most 14 are left-handed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) x 5 ?
Suppose that a simple random sample of n = 6 individuals is obtained from a population that is skewed right with mean u = 44 and standard deviation o =2. (a) The shape of the sampling distribution of the sample mean is approximately normal. Is this true or false? (b) What is the mean of the sampling distribution of the sample mean? (c) What is the standard deviation of the sampling distribution of the sample mean? (a) Choose the correct...
6. Let X1, . . . , Xn denote a random sample (iid.) of size n from some distribution with unknown μ and σ2-25. Also let X-(1/ . (a) If the sample size n 64, compute the approximate probability that the sample mean X n) Σηι Xi denote the sample mean will be within 0.5 units of the unknown p. (b) If the sample size n must be chosen such that the probability is at least 0.95 that the sample...
Select: less than, greater than or equal to
Let X have อ bnon ial distribution witn parameters n-25 and ρ Calculate each orthe following probabilities using the normal nation with the continuity correction to the cases ρ-0.5 0.6 and 0.8 and compare to the exact binomial probabilities calculated pro directly trarn the tarmula tar hn,p). (Round your answers ta tour decimal places.) (a) P(15X 20) P(15 s x s 20) P14.5 Normal 20.5) 0.S D.6 The nor nal approxim tion...
Let X have a binomial distribution with parameters n 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p-0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x;n, P). (Round your answers to four decimal places) (a) P15 s X 20) P P(1S s Xs 20) P(14.5 S Normal s 20.5) 0.5 0.6 0.8 The normal approximation of P(15 s X...
Suppose voters from a simple random sample of 500 (N
> 1,000,000) are interviewed and asked which presidential
candidate they're going to vote for. Of these, 35% say they'll vote
for the Statistics Party. You want to know the probability,
assuming this proportion is correct for the population, that more
than 40% of a random sample of 500 people will vote for the
Statistics Party. Which of these shows the three ways you could
find your answer?
A.
A-Using the...
: Let Yi, ½' . . . , Yn be an iid random sample from an exponential distribution with parameter where θ > 0. Here each Y, represents the lifetime of the ith battery, while θ represents the theoretical average lifetime. The pdf of each Y, is therefore given by fy (y) ei-1,2,...,n Consider the empirical average lifetime of the sample of n batteries given by Let a E R be a nonnegative real number. Consider the event A, defined...
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