BINOMIAL DISTRIBUTION

The probability of getting a bad orange from a box is 0.2. Christina has chosen 6 oranges. Calculate the probability that

(a) only one orange is bad.

(b) all the oranges are good.

• (a) 0.3351 (b) 0.2731

• (a) 0.4051 (b) 0.2831

• (a) 0.3932; (b) 0.2621

• (a) 0.4351 (b) 0.2731

In one report, 54% of Malaysians buy locally made cars. If 8 peoples who just bought new cars are selected at random, find the probability that

(a) at least 2 of them bought locally made cars,

(b) more than 6 of them bought locally made cars.

• (a) 0.9792; (b) 0.05650

• (a) 0.8192; (b) 0.15650

• (a) 0.8792; (b) 0.25650

• (a) 0.9192; (b) 0.15650

In a survey, it is found that 25% of the bulbs in a particular shop are spoilt. Find the probability that out of 10 bulbs,

(a) exactly 3 bulbs are spoilt,

(b) more than 8 bulbs are in good condition.

• (a) 0.2613; (b) 0.2540

• (a) 0.2503; (b) 0.2440

• (a) 0.3533; (b) 0.4440

• (a) 0.2563; (b) 0.2540

The probability that a school bus will be late to school is 0.15. Find the probability that in 5 school’s days, the bus will be late

(a) exactly 2 days, (b) at least once.

• (a) 0.1382 ; (b) 0.5563

• (a) 0.2372 ; (b) 0.5663

• (a) 0.1352 ; (b) 0.4563

• (a) 0.2682 ; (b) 0.4593

In a certain company, there are 3 out of 20 employees randomly selected, have life insurance. If there are 600 employees in the company, estimate the number of employees whose have the life insurance. Hence, calculate the variance.

• 90; 75.5

• 90; 76.5

• 90; 74.5

• 90; 73.5

A discrete random variable X has a binomial distribution, which is  $X\sim B\left(n,\ p\right)$   with a mean of 45 and a standard deviation of 3. Find the values of n and p.

• n = 54;  p = 0.8

• n = 56;  p = 0.6

• n = 54;  p = 0.6

• n = 56;  p = 0.8

A discrete random variable  $X\sim B\left(120,\ 0.4\right)$  . Find its mean and standard deviation.

• 46; 5.335

• 46; 5.337

• 48; 5.367

• 48; 5.467

There are 5 000 people in a village. It is found that 8 out of 10 of the villagers installed broadband at home. Find the mean, variance and standard deviation for the number of people who have broadband at home.

• 1 000; 800; 28.28

• 1000; 800; 26.26

• 4 000; 800; 28.28

• 4 000; 800; 26.26

Given that X is a binomial random variable with a mean and standard deviation of 4 and $\sqrt{3}$   respectively, calculate P(X =0).

• 0.01002

• 0.01023

• 0.02102

• 0.01102

80% of pupils in a certain school are interested in science. A sample consists of n pupils are randomly selected from the school. If the probability that all the pupils selected are interested in science is 0.1342, find the value of n.

• 7

• 8

• 9

• 10