17-24 - Calculating Binomial Coefficients Evaluate the expression. () 6. 8 18. 100 -17. () 19. 98 10 5 20. 21. 22. 5 3 • (:) • () • (:) • () - () (:) - (1) - (?) - (;) - (;) –- (:) 23. 24. 3.
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- What is the Binomial Theorem and what is its use?Q6. Regarding Normal Approximation to the Binomial, one rule states that the Normal Approximation begins to apply when the products of n, p, and q is equal to 10 or more. True False None of the aboveRegarding Normal Approximation to the Binomial, one rule states that the Normal Approximation applies when the products of n, p, and q is equal to 4. A. TrueB. FalseC. None of the above
- Q1. Regarding Normal Approximation to the Binomial, one rule states that the Normal Approximation applies when the products of n, p, and q is equal to 5 or more. TrueB. False C. None of the aboveRecords show that the probability is 0.0012 that a per-son will get food poisoning spending a day at a certain state fair. Use the Poisson approximation to the binomialdistribution to find the probability that among 1,000 per-sons attending the fair at most 2 will get food poisoning."Statistically Z-Test can be used if the sample is large ( n > 30 ) even population SD is not given". Justify this statement either by proving algebraically or computation.
- Q-1 Consider a binomial experiment with n = 20 and p = .70. Compute f(16). Q-2 Consider a binomial experiment with n = 20 and p = .70. Compute P(x ≥ 16). Q-3 Consider a binomial experiment with n = 20 and p = .70. Compute P(x ≤ 15). Q-4 Consider a binomial experiment with n = 20 and p = .70. Compute E(x). Q-5 Consider a binomial experiment with n = 20 and p = .70. Compute Var(x) and σWomen executives A company is criticized because only13 of 43 people in executive-level positions are women.The company explains that although this proportion islower than it might wish, it’s not surprising given thatonly 40% of all its employees are women. What do you think? Test an appropriate hypothesis and state your con-clusion. Be sure the appropriate assumptions and condi-tions are satisfied before you proceed.Using excel functions consider a binomial experiment with n=20 and p=.7a. Compute P(x ≥ 15)b. Compute E[x]C. Compute Var [x] and
- A lot of parts contains 500 items, 100 of which are defective. Suppose that 20 items are selected at random. Let X be the number of selected items that are defective. a) Express the quantity P(X = 5) using factorials. b) Use the binomial approximation to compute an approximation to P(X = 5).When calculating all the values of a binomial distribu-tion, the work can usually be simplified by first calculating b(0; n, θ ) and then using the recursion formulab(x + 1; n, θ ) = θ (n − x) (x + 1)(1 − θ ) · b(x; n, θ )Verify this formula and use it to calculate the values ofthe binomial distribution with n = 7 and θ = 0.25.Suppose that historically, 35% of applicants that are offered admittance to Texas Tech actually enroll, while the others take offers somewhere else. If Texas Tech will accept 9300 this coming year, what is the probability that less than 3250 will actually enroll? Use the normal approximation to the binomial. P(X < 3250)
