# Lesson Worksheet: Approximating a Binomial Distribution Mathematics

In this worksheet, we will practice approximating a binomial distribution with a normal distribution.

Q1:

Which of the following four binomially distributed random variables may be approximated by a normal distribution?

• Aa and b
• Ba and c
• Cb and c
• Db and d
• Ea and d

Q2:

is a binomially distributed random variable, and . Write down a normal approximation of , stating the values of and .

• A
• B
• C
• D
• E

Q3:

A discrete random variable is binomially distributed, and . Using a normal approximation, estimate .

Q4:

A discrete random variable is binomially distributed, and . Using a normal approximation, estimate .

Q5:

A discrete random variable is binomially distributed, and . Using a normal approximation, estimate .

Q6:

A discrete random variable is binomially distributed, and . Using a normal approximation, estimate .

Q7:

Matthew flips a fair coin 84 times. By using a suitable normal approximation, calculate the estimated probability that the coin lands on heads more than 50 times.

Q8:

A farm produces eggs. The farmer claims that of the eggs weigh more than 64 grams. A random sample of 20 eggs is taken. Find the exact probability that at least 15 of the eggs weigh more than 64 grams.

A random sample of 1,000 eggs is taken. Use a normal approximation to estimate the probability that more than 550 and less than 600 eggs weigh more than 64 grams.

Q9:

Some seeds are planted. The probability that a particular seed will germinate after 4 days is . Of a random sample of 10 seeds, find the exact probability that 7 of the seeds will germinate after 4 days.

A normal approximation predicts a probability of 0.65 that at least seeds will germinate from a random sample of 300 seeds. Find the value of .

• A171
• B161
• C181
• D195
• E105

Q10:

A population of frogs contains female and male frogs in the ratio . A random sample of 100 frogs is taken. Find the percentage error when using a normal approximation to calculate the probability that exactly 60 of the frogs are female.

• A
• B
• C
• D
• E