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
yKpoI14uk [10]
3 years ago
5

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper

containers. An employee, John Halstrom, randomly selects 14 of these containers of paper. What is the probability that John finds less than 7 golden sheets of paper? Round your answer to two decimal places.
Mathematics
1 answer:
Korvikt [17]3 years ago
7 0

Answer:

90.67% probability that John finds less than 7 golden sheets of paper

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it contains a golden sheet of paper, or it does not. The probability of a container containing a golden sheet of paper is independent of other containers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper containers.

This means that p = 0.3

14 of these containers of paper.

This means that n = 14

What is the probability that John finds less than 7 golden sheets of paper?

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{14,0}.(0.3)^{0}.(0.7)^{14} = 0.0068

P(X = 1) = C_{14,1}.(0.3)^{1}.(0.7)^{13} = 0.0407

P(X = 2) = C_{14,2}.(0.3)^{2}.(0.7)^{12} = 0.1134

P(X = 3) = C_{14,3}.(0.3)^{3}.(0.7)^{11} = 0.1943

P(X = 4) = C_{14,4}.(0.3)^{4}.(0.7)^{10} = 0.2290

P(X = 5) = C_{14,5}.(0.3)^{5}.(0.7)^{9} = 0.1963

P(X = 6) = C_{14,6}.(0.3)^{6}.(0.7)^{8} = 0.1262

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0068 + 0.0407 + 0.1134 + 0.1943 + 0.2290 + 0.1963 + 0.1262 = 0.9067

90.67% probability that John finds less than 7 golden sheets of paper

You might be interested in
What do you add to 2 3/8 to make 6
scoundrel [369]
29 because first u add 5 then 8 3 times.
7 0
3 years ago
Six friends equally share a bag of popcorn. The bag contains 9 cups of popcorn. How many cups of popcorn should each friend get?
nadya68 [22]
Six friend =6
A bag popcorn = 9
Share equally 9/6 = 1.5 bag for each person
7 0
3 years ago
Read 2 more answers
Plz ASAP i will give you brainliest and you will get a lot of points
saul85 [17]

Answer:

1 inch to 4: 12 to 28

the second one: 8 to 128

The third one: 5 to 125

The fourth one: 13 to 117

Step-by-step explanation:

if that makes sense, I hope this will help

8 0
3 years ago
Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometers (x) she can drive on 22 liters of fu
LenaWriter [7]

Answer:

I don't know

Step-by-step explanation:

thanks for the pints

6 0
3 years ago
Read 2 more answers
What is the value of n?
Sliva [168]

Answer:

D

Step-by-step explanation:

5n=85

n=17

3 0
3 years ago
Read 2 more answers
Other questions:
  • Alberto spent half of his weekly
    12·1 answer
  • What is the slope of this graph? A. −14 B. 4 C.−4 D. 14
    10·2 answers
  • Number 16 what is the answer
    5·2 answers
  • Simplify the following expressionn.
    9·2 answers
  • Subtract the mixed numbers.<br> 15 5/7 − 6 4/5
    15·2 answers
  • Write an equation to solve this problem:
    5·1 answer
  • A student wants to write an expression for, "all of the elements which are not in set
    11·1 answer
  • Plz Um can someone Please help me I really need help with this
    7·1 answer
  • HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
    12·1 answer
  • Solve the equation. Then check your solution
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!