The masses, in grams, of chocolate bars produced by a factory can be modelled by a normal distribution with mean 100g and standard deviation 0.6g. A chocolate bar can only be packaged if its mass is greater than 99g, otherwise is it melted back into the production line.

On a given day, the number of chocolate bars packaged is 5000.

James is sitting a multiple choice exam with 15 questions. Each question has 3 answer choices, of which only one is correct.

James randomly picks an answer on each question. Let X represent the number of questions James answers correctly.

On a penalty kick, Bob scores a goal 75% of the time. Over the course of a game, Bob kicks 8 penalty kicks.

A facial‑recognition access system is used to admit staff into a secure facility, but it is not perfectly reliable. When a registered employee presents themselves, there is a 15% chance the system will reject them. Each scan is independent of the others.

Twelve employees attempt entry and all are registered users.

An electronics factory uses an automated inspection system to test non‑defective circuit boards. Each board has a 10% chance of being incorrectly rejected by the machine, and each test is independent.

A batch of 20 non‑defective boards is inspected.

The following table shows the distribution of a random variable X.

The following diagram shows the curve of the normal distribution of the random variable X.

The area of the shaded region R is 0.32.

It is given that P(X>58)=0.68.

The probability distribution of a discrete random variable X is shown in the following table.

At a local carnival, players can pay 6 tokens to play Lucky Spinner. Each turn, the player spins a wheel with segments numbered 0-4. If the wheel lands on s, the player wins s2 tokens.

The following table shows the distribution S of spins s.

It is given that the game is fair.

Let L∼B(5,p) be the random variable representing the number times a player loses money in 5 turns.