If X has a Hypergeometric distribution with sample size (n) = 10, the number of successes in the population (A) = 12, and the population size (N) = 25, then P(X < 3) = ________.
Answer:
Given,
n = 10
A = 12
N = 25
Consider,
P(X = k) = ACk * (N-A)C(n-k) / NCn
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= 12C0*13C10 / 25C10 + 12C1*13C9 / 25C10 + 12C2*13C8 / 25C10
= 1*286 / 3268760 + 12*715 / 3268760 + 66*1287 / 3268760
= 1/3268760 (286 + 8580 + 84942)
= 96808 / 3268760
= 0.0287
If X has a Hypergeometric distribution with sample size (n) = 10, the number of successes...
Below, n is the sample size, p is the population proportion of successes, and X is the number of successes in the sample. Use the normal approximation and the TI-84 Plus calculator to find the probability. Round the answer to at least four decimal places. ol. F loa n=88, p=0.49 P(x>36)
Conduct a study to determine how well the binomial distribution approxi mates the hypergeometric distribution. Consider a bag with n balls, 25% of which are red. A sample of size (0.10)n is taken. Let X be the number of red balls in the sample. Find P(X (0.02)n) for increasing values of n when | sampling is (i) with replacement and (i) without replacement. Use R
Conduct a study to determine how well the binomial distribution approxi mates the hypergeometric distribution....
7, Random variable X has a hypergeometric distribution with N= 25, n = 4, and K = 4. Determine the following: a) E(X) b) V(X) c) P(X- 1) d) P(X-4) e) P(X2
1.Given below are the number of successes and sample size for a simple random sample from a population. x= 7, n = 50, 98% level. the 98% confidence interval is from _ to _.
The number of successes and the sample size are given for a simple random sample from a population. Use the one-proportion plus-four z-interval procedure to find the required confidence interval. n = 188, x = 157; 95% level 0.785 to 0.871 0.786 to 0.870 0.774 to 0.882 0.775 to 0.881
Suppose x has a distribution with μ = 10 and σ = 2. (a) If a random sample of size n = 39 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(10 ≤ x ≤ 12) = (b) If a random sample of size n = 56 is drawn, find μx, σ x and P(10 ≤ x ≤...
A random variable, \(x\), has a hypergeometric distribution with \(\mathrm{N}=13, X=9\), and \(n=4\).a. Calculate \(\mathrm{P}(\mathrm{x}=3)\).b. Calculate \(\mathrm{P}(\mathrm{x}=6)\).c. Calculate \(\mathrm{P}(x \geq 4)\).d. Find the largest \(x^{\prime}\) so that \(P\left(x>x^{\prime}\right)>0.25\).a. The probability is (Round to four decimal places as needed.)
Suppose that a simple random sample of size n = 400 selected from a population has x = 247 successes. Calculate the margin of error for a 95% confidence interval for the proportion of successes for the population, p. Compute the sample proportion, p, standard error estimate, SE, critical value, z, and the margin of error, m. Use a z-distribution table to determine the critical value. Give all of your answers to three decimal places except give the critical value,...
Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 90, p = 0.56: P(45 < X < 58) Group of answer choices 0.0655 0.7853 0.1492 0.9345
The number of successes and the sample size for a simple random sample from a population are given. a. Determine the sample proportion. b. Decide whether using the one-proportion z-interval procedure is appropriate. c. If appropriate, use the one-proportion z-interval procedure to find the confidence interval at the specified confidence level x-75, n-250, 95% level a. What is the sample proportion? b. Is the one-proportion z-interval procedure appropriate? OA. No, because x is less than 5. O B. Yes, because...