1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ArbitrLikvidat [17]
3 years ago
5

An experiment consists of 8 independent trials where the probability of success on each trial is 3 8 . Find the probability of o

btaining the following. Round answers to the nearest ten-thousandth. 13. Exactly 3 successes. 14. Exactly 6 successes. 15. Exactly 1 success. 16. Exactly 5 successes. 17. At least 1 success. 18. At least 2 successes. 19. At least 6 successes. 20. At least 7 successes. 21. At most 7 successes. 22. At most 6 successes
Mathematics
1 answer:
Rzqust [24]3 years ago
7 0

Answer:

Step-by-step explanation:

This is a binomial distribution because the probabilities are either that of success or failure.

If probability of success, p = 3/8 = 0.375, then probability of failure, q = 1 - p = 1 - 0.375 = 0.625

The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = represents the probability of failure.

n represents the number of trials or sample.

n = 8

13) P(x = 3) = 8C3 × 0.375^3 × 0.625^(8 - 3) = 0.28

14) P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03

15) P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11

16) P(x = 5) = 8C5 × 0.375^5 × 0.625^(8 - 5) = 0.1

17) P(x ≥ 1) = 1 - P(x < 1)

P(x < 1) = P(x = 0)

P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023

P(x ≥ 1) = 1 - 0.023 = 0.977

18) P(x ≥2) = 1 - P(x < 2)

P(x < 2) = P(x = 0) + P(x = 1)

P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023

P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11

P(x ≥ 2) = 1 - (0.023 + 0.11) = 0.867

19) P(x ≥ 6) = P(x = 6) + P(x = 7) + P(x = 8)

P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03

P(x = 7) = 8C7 × 0.375^7 × 0.625^(8 - 7) = 0.005

P(x = 8) = 8C8 × 0.375^8 × 0.625^(8 - 8) = 0.0004

P(x ≥ 6) = 0.03 + 0.005 + 0.0004 = 0.0354

20) P(x ≥ 7) = P(x = 7) + P(x = 8)

P(x ≥ 7) = 0.005 + 0.0004 = 0.0054

21) P(x ≤ 6) = 1 - P(x = 8)

P(x ≤ 6) = 1 - 0.0004 = 0.9996

22) P(x ≤ 6) = 1 - [P(x = 7) + P(x = 8)]

P(x ≤ 6) = 1 - (0.005 + 0.0004) = 0.9946

You might be interested in
Mrs. Kidd is five feet 3 inches tall. If one inch is approximately 2.5 centimeters, how many centimeters tall is Mrs. Kidd? Do N
Arturiano [62]

Answer:

Mrs.kidd is 162.5 centimeters tall

Step-by-step explanation:

5 foot 3 inches is 63 inches

63 times 2.5 = 162.5

Mrs.kidd is 162.5 centimeters tall

7 0
3 years ago
Giúp em nhanh ạ <br><br>(x+2)(x−2)−(x−3)(x+5)=0
Ivenika [448]

Answer:

x=11/2

Step-by-step explanation:

4 0
2 years ago
Chris and Mikala each got a candy bar that were the same size. Chris cut his
bazaltina [42]

Answer:

Chris ate more of his candy bar

6 0
3 years ago
If you make 8$ an hour and get a 10% raise what is your new hourly pay?
statuscvo [17]
Answer: 2.2% I’m not sure (ps. I’m really not sure like this is what I think it is butttt someone’s answer might be better so go with there’s)
5 0
2 years ago
-6x - 2x = 40. Calculate and show work
xxMikexx [17]
-6x-2x= 40
-8x=40
X= 40/-8
X= -5
3 0
3 years ago
Read 2 more answers
Other questions:
  • In need of some help please.
    10·1 answer
  • Write an equation of the line slope= -1; (2, 0)
    15·1 answer
  • Tan ^-1 (-1). enter your answer in radians
    15·1 answer
  • Scaling Question 2 Which describes the product when two fractions greater than 0 and less than 1 are multiplied? Your answer: Th
    13·1 answer
  • Which value from the set {5, 10, 15, 50} makes k/5 = 10 true?
    11·1 answer
  • Simplify the expression<br><br><br> 2(6x + 3)
    12·1 answer
  • The least-squares regression line is: Group of answer choices a. the line that passes through the most data points. b. the line
    14·1 answer
  • Danielle sells 3 donuts for $9. Write an equation to represent the relationship between the number of donuts sold and the earnin
    8·1 answer
  • Hannah has an offer from a credit card issuer for 0% APR for the first 30 days
    7·2 answers
  • PLS help,269 divided by 4​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!