The random variable $X\sim B(400,0.54)$.

Use a suitable approximation to estimate the value of $P(X\ge 222)$.

Give your answer correct to 3 significant figures.

The random variable $X\sim B(500,0.52)$.

Use a suitable approximation to estimate the value of $P(X\le 242)$.

Give your answer correct to 3 significant figures.

The random variable $X\sim B(400,0.45)$.

Use a suitable approximation to estimate the value of $P(X\le 185)$.

Give your answer correct to 3 significant figures.

The random variable $X\sim B(600,0.58)$.

Use a suitable approximation to estimate the value of $P(348\le X\le 352)$.
Give your answer correct to 3 significant figures.

John buys boxes of chocolates. $58\mathrm{\%}$ of boxes have 12 chocolates or more in them.

John buys 180 boxes.

Use a normal approximation to find the probability that less than $85$ boxes will have 12 chocolates or more.

Give your answer correct to 3 significant figures.

The random variable $X\sim B(740,0.46)$.

Use a suitable approximation to estimate the value of $P(X=360)$.
Give your answer correct to 3 significant figures.

A fair coin is thrown $180$ times.

Use a suitable approximation to estimate the probability of getting more than $100$ Tails.

Give your answer correct to 3 significant figures.

A fair coin is thrown $250$ times.

Use a suitable approximation to estimate the probability of getting less than $115$ Tails.

Give your answer correct to 3 significant figures.

A factory produces sweets and an employee noticed that 46% of the sweets have an irregular shape.

A sample of $800$ sweets is taken.

Use a normal approximation to find the probability that between $360$ and $370$ sweets will have an irregular shape.

Give your answer correct to 3 significant figures.

A school sells pencil cases. $54\mathrm{\%}$ of the pencil cases have an extra ruler in them.

The school sold $150$ pencil cases in September.

Use a normal approximation to find the probability that more than $80$ pencil cases had the extra ruler.

Give your answer correct to 3 significant figures.