Checking Requirement The SAT test uses multiple-choice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. We want to find the probability of getting exactly 10 correct answers for someone who makes random guesses for answers to a block of 25 questions. If we plan to use the methods of this section with a normal distribution used to approximate a binomial distribution, are the necessary requirements satisfied? Explain.

Problem 4BSC

Answer:

Step1 of 3:

We have The SAT test uses multiple-choice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. We want to find the probability of getting exactly 10 correct answers for someone who makes random guesses for answers to a block of 25 questions.

That is n = 25 S = {a, b, c, d, and e}

p = P(probability of getting correct answer) =

Therefore, p = 0.2

q = 1 - p

= 1 - 0.2

= 0.8

Therefore, q = 0.2

Step2 of 3:

We need to check are the necessary requirements of approximation of binomial distribution satisfied?

Step 3 of 3:

Consider,

The necessary requirements of approximation of binomial distribution is given by

1).np5

2).nq5

Now,

1).np = 250.2

= 5

Here, np = 5.

Hence, condition (1) satisfied.

2).nq = 250.8

= 20

Here, nq = 20.

Hence, condition (2) also satisfied.

Therefore,the necessary requirements of approximation of binomial distribution is satisfied.