Topic 4.8: Binomial Distribution Questions

Write down the distribution of $X$.

X ~ B(6, 0.5). Find P(X = 4).

X ~ B(15, 0.2). Find P(X ≤ 4) using a GDC.

A test has 8 true/false questions answered by guessing. Write down the distribution of the number of correct answers X.

State the four conditions required for a binomial distribution.

X ~ B(12, 0.25). Find P(X = 0).

X ~ B(50, 0.6). Find the mean and explain what it represents.

Show that the mean of $X$ is $3$.

Find the mean of $X$.

X ~ B(20, 0.3). Write down the mean of X.

In a factory, 10% of light bulbs are faulty. A random sample of 12 bulbs is taken. Let X be the number of faulty bulbs.

A multiple-choice section has 40 questions. A student answers each one correctly with probability 0.65, independently. Let X be the number of correct answers.

(a) Find the mean of X.

(b) Find the standard deviation of X.

X ~ B(10, 0.4). Find P(X ≥ 5).

Explain why the number of red cars passing a point in one hour is NOT necessarily a binomial variable.

A spinner lands on red with probability 0.4. It is spun 8 times. Let X be the number of times it lands on red.

The probability a seed germinates is 0.8. In a tray of 10 seeds, find the probability that at least 9 germinate.

A quiz has 10 multiple-choice questions, each with 4 options and exactly one correct answer. A student guesses every answer at random. Let X be the number of correct answers.

At a bakery, each loaf is slightly burnt with probability 0.06, independently of the others. A baker boxes 25 loaves. Let X be the number of burnt loaves in the box.

(a) Write down the expected number of burnt loaves.

(b) Find the probability that at least one loaf in the box is burnt.

A spam filter wrongly flags a genuine email as spam with probability 0.12, independently for each email. In one folder there are 18 genuine emails. Let X be the number wrongly flagged as spam.

(a) Find the probability that exactly 3 emails are wrongly flagged.

(b) Find the probability that at most 2 emails are wrongly flagged.

A multiple-choice quiz has 12 questions, each with four options. A student guesses every answer, so each question is answered correctly with probability 0.25. Let X be the number of successes.