Topic 4.8: Binomial Distribution Questions

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

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

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

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

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

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.

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.

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.

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.

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

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

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

X ~ B(10, 0.4). Find P(X ≥ 5).

On a commuter line, each train is late with probability 0.3, independently. A passenger records 20 journeys. Let X be the number of late trains.

(a) Find the probability that at least 8 trains are late.

(b) Find the probability that between 4 and 7 trains inclusive are late.

A basketball player has a 70% chance of scoring each free throw, independently. She takes 5 free throws. Let X be the number she scores.