IB Applications Probability

A machine fills plastic bottles with mineral water. The volume of mineral water that the machine pours into each bottle follows a normal distribution with the mean of 498ml and a standard deviation of 3.4ml. Each bottle has a maximum capacity of 506ml. On the label of each bottle is printed the statement: Contents 500ml.

Find the probability that a bottle chosen by random has a volume less than 500 ml

• 0.278

• -0.278

• 0.722

• 0.498

Is the distribution below a probability distribution? Why or why not?

• Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1

• No, not all P(x) values are between 0 and 1.

• No, ∑P(x) ≠ 1.

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct?

• 0.962

• 0.132

• 0.831

• 0.250

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood? 

• 0.088

• 0.697

• 0.214

• 0.303 

When rolling two dice, the probability of rolling doubles is 1/6. Suppose that a game player rolls the dice four times, hoping to roll doubles. What is the probability the player gets doubles more than twice in 4 attempts?

• 0.016

• 0.00077

• 0.132

• 0.004

Bob is taking a 100 question test.  They have a 90 % probability of getting any one question correct.  WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that they will answer EXACTLY 70  questions correctly?

• ₁₀₀C₇₀   ( 0.18  )³⁰ ( 0.90  )⁷⁰
  

• ₁₀₀C₇₀   ( 0.10  )³⁰ ( 0.90  )⁶⁰

• ₁₀₀C₇₀   ( 0.10  )³⁰ ( 0.90  )⁷⁰

• ₉₉C₇₀   ( 0.10  )³⁰ ( 0.90  )⁷⁰

Find the mean of a binomial distribution with n=50 and p=0.4

• 50

• 4

• 20

• 10