I want answer to these question qickly Find P(x lessthanorequalto k) for each of

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I want answer to these question qickly

Find P(x lessthanorequalto k) for each of the following case. (a) n = 20, p = 0.15, k = 2 (b) n = 15, p = 0.7, k = 8 (c) n = 10, p = 0.8, k = 9 A jar contains five balls three red and two white. Two balls are randomly selected without replacement from the jar, and the number x of red ball is recorded. Explain why x is or is not a binomial random variable. If the experiment is binomial, give the values of n and p. The random variable x is not a binomial random variable since there is an unequal number of a red and white ball in the jar. For this reason, the probability p of choosing a red ball changes from trial to trial. The random variable x is a binomial random variable since the balls are selected without replacement. The value of p is 0.2 and n is 5. The random variable x is a binomial random variable since the balls are selected without replacement. The value of p is 0.6 and n is 5. The random variable x is not a binomial random variable since the balls are selected without replacement. For this reason, the probability p of choosing a red ball changes from trial to trial. The random variable x is a binomial random variable since there is an unequal number of a red and white ball in the jar. The value of p is 0.2 and n is 3. In 2010, the average overall SAT score (Critical Reading, Math, and Writing) for college-bound students the United Stat was 1509 out of 2400. Suppose that 30% of all high school graduates took this test, and that 400 high school graduates are randomly selected from throughout the United States. Which of the following random variables has an approximate binomial distribution? If possible, give the values for n and p. (If not possible, enter IMPOSSIBLE). (a) The number of students who took the SAT. This is a binomial random variable. This is not a binomial random variable. n = p = (b) The scores of the 400 students on the SAT. This is a binomial random variable. This is not a binomial random variable. n = p = (c) The number of students who scored above average on the SAT. This is a binomial random variable. This is not a binomial random variable. n = p = (d) The amount of time it took the students to complete the SAT. This is a binomial random variable. This is not a binomial random variable. n = p =

Explanation / Answer

3.

We will use the binomial distribution pdf function to solve the problem:

a. P(X<=2) = 20C0(.15^20)(.85^0)+ 20C0(.15^19)(.85^1)+ 20C2(.15^18)(.85^2) = 0.405

b. P(X<=8) = 20C0(.15^20)(.85^0)+..20C8(.15^8)(.85^12) = 0.1311

c. P(X<=9) = 20C0(.8^0)(.2^20) +..+20C9(.8^9)(.2^11) = 0.8926

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