Let
The expected value (Mean) of is given by
Hence
The variance of is
Given that
The mean of is
The variance of is
The standard deviation of is
Using CLT, we know that has a normal distribution with mean and standard deviation
The probability using CLT, without using the correction factor is
The probability using CLT, with correction factor is
Each of Xs have 1 success, and hence can see that there are 16 successes in . That is is the number of trials required to get 16 successes, with probability of success on any given trial p=0.5.
We can say that has negative binomial distribution with parameters, number of successes =16 and the probability of success p=0.5
The pmf of is
The exact probability is
The CLT estimate with the correction is 0.0918 and without the correction is 0.0793.
Hence we can say that the CLT underestimates the exact probability.
Find the mean of S16. Find the standard deviation of S16. (Round it to one decimal place) Find P(S16 > 40) using CLT, without correction factor. (Round it to 4 decimal places) Find P(S16 >...
Find the mean of S16. Find the standard deviation of S16. (Round it to one decimal place) Find P(S16 > 40) using CLT, without correction factor. (Round it to 4 decimal places) Find P(S16 > 40) using CLT, with correction factor. (Round it to 4 decimal places FIND p0=exact = P(S16 > 40). Note This is negative binomial with number of successes = n. Do not use Mathematica. It gives different answer because its definition of Negative Binomial is slightly different...
S16 = sigma Xi where (X1,X2 ... X16) iid geometric each with mean 2 Find mean of S16: Find standard deviation of S16: Find P(S16 > 40) using Central Limit Theorem, without correction factor: Find P(S16 > 40) using Central Limit Theorem, with correction factor: Find p0 = exact = P(S16 > 40)
Find exact value p0 = P(S16 = 16). (round your answer to four decimal places). Use CLT to approximate p0. Assume the answer is equal to p1 (round your answer to four decimal places). Is p1 an over estimate or underestimate or equal up to 4 decimal places? Let S16-Σ Xi where {X1, X2, , X16} iid Poisson each with mean 1 Let S16-Σ Xi where {X1, X2, , X16} iid Poisson each with mean 1
Find the mean of this probability distribution. Round your answer to one decimal place. x P(x) 0 0.1 1 0.1 20.05 30.75 Find the mean of this probability distribution. Round your answer to one decimal place. Preview
Find the mean of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.μ=32μ=32 and σ=6σ=6; n=9
Please do all 3 problems 1. Find C(n, x)pxqn − xfor the given values of n, x, and p. (Round your answer to four decimal places.) n = 6, x = 5, p = 0.7 2.Let X be the number of successes in six independent trials of a binomial experiment in which the probability of success is p = 2/5. Find the following probabilities. (Round your answers to four decimal places.) (a) P(X = 5) (b) P(2 ≤ X ≤...
Check My Worl eBook New York City is the most ex standard deviation of $55. Use Table 1 in Appendix B in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distribute What is the probability that a hotel room costs $225 or more per night (to 4 decimals)? 0.3513 b. What is the probability that a hotel room costs less than $140 per...
Suppose x has a distribution with a mean of 40 and a standard deviation of 20. Random samples of size n = 64 are drawn. (a) Describe the x bar distribution. x bar has a normal distribution. x bar has a geometric distribution. x bar has an approximately normal distribution. x bar has a Poisson distribution. x bar has an unknown distribution. x bar has a binomial distribution. Compute the mean and standard deviation of the distribution. (For each answer,...
A. Compute the test statistic x2=_____ (Round to three decimal places) Find the P-value=______ (Round to three decimal places) Reject/Fail To reject _____ H0. There is/is not_____ sufficient evidence to warrant rejection of the claim that pulse rates of women have a standard deviation equal to 10 beats per minute. B. Find the test statistic= x2=_____ (Round to three decimal places) Find the p-value of test statistic=_______ (Round to three decimal places) (1) _________H0. There(2)__________sufficient evidence to conclude that the...
A. Identify the test statistic=_____ (Round to two decimal places) The P-value is=_____ (Round to three decimal places) What is the concluion for this hypothesis test? A. Fail to reject Upper H0. There is sufficient evidence to warrant rejection of the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150. B. Reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the variation of...