IB Math Applications -Binomial &Normal distributions

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.

Tags

CCSS.HSS.MD.A.1

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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

Tags

CCSS.HSS.CP.B.9

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 

Tags

CCSS.HSF-LE.A.1C

4. 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

Tags

CCSS.HSS.CP.B.8

CCSS.HSS.CP.B.9

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

Tags

CCSS.HSS.CP.B.9

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

• 50

• 4

• 20

• 10

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

Find the variance of a binomial distribution with 50 trials and p= 0.4

• 12

• 15

• 10

• 20

Find the standard deviation of a binomial distribution with n=50 and p=0.4 (Round to the nearest tenth)

• 4.2

• 3.5

• 12.0

• 6.2

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 22%.

• 69.37 in 
• 67.58 in 
• 73.12 in 

Tags

CCSS.HSS.ID.A.4