Binomial Distribution

A small college has 800 students, 10% of which are left-handed. Suppose they take an SRS (simple random sampling) of 8 students. Let L be the number of left-handed students in the sample.

What is P(L = 2)?

Write your answer in 3 significant figures.

Salim has a flock of 300 chickens, 15% of which are infected with a virus. He plans on taking an SRS (simple random sample) of 7.
Find the probability that exactly 4 of the 7 chickens sampled have the virus.

Write your answer in 3 significant figures. 

An online retailer offers next-day shipping for an extra fee. The retailer says that 95% of customers who pay for next-day shipping actually receive the item the next day, and those who don't are issued a refund. Suppose we take an SRS(simple random sample) of 20 next-day orders, and let X represent the number of these orders that arrive the next day. Assume that the arrival statuses of orders are independent.

What is P(X = 19)?

Write your answer in 3 significant figures.

Biologists breed a pair of plants where each plant has the color genes Gg. This means that any offspring these plants produce has a 25% chance of inheriting the color genes gg, which makes the offspring an albino plant. Assume that offspring inherit genes independently from each other.

Find the probability of this pair producing exactly 1 albino plant among 6 offspring.

Write your answer in 3 significant figures.

Marta makes 90% of the free throws she attempts. She is going to shoot 3 free throws. Assume that the result of free throws are independent from each other. Let X represent the number of free throws she makes.

Find the probability that Marta makes at least 2 of the three free throws.

Write your answer in 3 significant figures.

Suppose that 80% of trees in a forest of 300 trees are infected with a virus, and we take an SRS of 5 rees to test for the virus.

What is the probability that exactly 2 of the 5 trees have the virus?

Write your answer in 3 significant figures.

Aja's favorite cereal is running a promotion that says 1-in-4 boxes of the cereal contain a prize. Suppose that Aja is going to buy 5 boxes of this cereal, and let X represent the number of prizes she wins in these boxes. Assume that these boxes represent a random sample, and assume that prizes are independent between boxes.

What is the probability that she wins at most 1 prize in the 5 boxes?

Write your answer in 3 significant figures.

An egg supplier to a restaurant sends a daily shipment of 500 eggs. Previous records show that 4% of these eggs arrive damaged to the restaurant. Let X = the number of eggs that arrive damaged on a randomly selected day.

Find the mean and standard deviation of X.

Answers must be in 3 significant figures.

• Mean=20

  SD = 4.38

• Mean = 2000

  SD = 34.6

• Mean = 200

  SD = 11.0

• Mean = 2

  SD = 1.41