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
DiKsa [7]
3 years ago
10

Historically 80% of the monitors made by your company will pass your stringent quality control checks. 40 monitors have just com

e off the assembly line.a) What is the probability that exactly 30 of them will pass the quality control checks?b) What are the expected value and variance of the number of these monitors that will pass the quality control checks?
Mathematics
1 answer:
madam [21]3 years ago
4 0

Answer:

a) 10.75% probability that exactly 30 of them will pass the quality control checks.

b) Expected value is 32

Variance is 6.4

Step-by-step explanation:

For each monitor, there are only two possible outcomes. Either they will pass the quality checks, or they will not pass these checks. The probability of a monitor passing these checks is independent of other monitors. 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.

The expected value of the binomial distribution is:

E(X) = np

The variance of the binomial distribution is:

V(X) = np(1-p)

80% of the monitors made by your company will pass your stringent quality control checks.

This means that p = 0.8

40 monitors have just come off the assembly line.

This means that n = 40

a) What is the probability that exactly 30 of them will pass the quality control checks?

This is P(X = 30). So

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

P(X = 30) = C_{40,30}.(0.8)^{30}.(0.2)^{10} = 0.1075

10.75% probability that exactly 30 of them will pass the quality control checks.

b) What are the expected value and variance of the number of these monitors that will pass the quality control checks?

E(X) = np = 40*0.8 = 32

Expected value is 32

V(X) = np(1-p) = 40*0.8*0.2 = 6.4

Variance is 6.4

You might be interested in
What are the solutions of the following equation?
noname [10]

Answer:

D. x = 7 and x = 14

Step-by-step explanation:

this is a quadratic equation, so use the quadratic formula: (-b+-√b^2-4ac) / 2a for ax^2+bx+c=0

7 0
3 years ago
What is the distributive property of 75x6
ohaa [14]
That would be 60 and 15
5 0
2 years ago
Read 2 more answers
What is the perimeter of this shape? Use numbers only.
aniked [119]

Answer:

30 m

Step-by-step explanation:

You simply add the lengths of all the sides. 3 m is not needed for this.

8 0
2 years ago
Read 2 more answers
Find the range of y = -3x + 7 for the domain {-8, -6, -3, -2, 2}
svetlana [45]
The domain is the set of x-values of a function. The range is the set of y-values of a function.

You are told that the domain, or x-values, are -8, -6, -3, -2, and 2. To find the range, you just need to plug in each of the x-values into the function <span>y = -3x + 7 and find the value of y.
1) When x = -8:
</span><span>y = -3x + 7
y = -3(-8) + 7
y = 24 + 7
y = 31

2) When x = -6
</span>y = -3x + 7
y = -3(-6) + 7
y = 18 + 7
y = 25

3) When x = -3
y = -3x + 7
y = -3(-3) + 7
y = 9 + 7
y = 16

4) When x = -2
y = -3x + 7
y = -3(-2) + 7
y = 6 + 7
y = 13

5) When y = 2
y = -3x + 7
y = -3(2) + 7
y = -6 + 7
y = 1

The range is {31, 25, 16, 13, 1}.

-------

Answer: 
{31, 25, 16, 13, 1}
5 0
3 years ago
Hi. Sorry this is bad quality. <br><br> What is the slope of the line on the graph?
d1i1m1o1n [39]
Slope (m) =0

θ =180°

distance (d) =15

ΔX =15

ΔY =0
5 0
2 years ago
Other questions:
  • 2. A researcher collected data about the favorite car color of a particular population. He asked 250 people about their favorite
    15·1 answer
  • What is −2 1/4 ⋅ (−2 13) ?<br><br><br> A −5 1/4<br> B −4 1/12 <br> C 4 1/12 <br> or D 5 1/4
    14·1 answer
  • A carpenter cut the top section of a window frame with a 37° angle on each end. The side pieces each have a 50° angle cut at the
    8·2 answers
  • Which equation can be used to find the measure of an angle that is supplementary to ∠
    15·1 answer
  • Can You please help me cause I'm gangsta Simplify (5^-2)^4 ​
    5·1 answer
  • June bought ​ 3 1/2 ​ gallons of white paint at $17.50 per gallon and ​ 1 3/4 gallons of blue paint at $19.00 per gallon. What w
    15·2 answers
  • 2. Is the following quadratic equation in Vertex form?<br> y = - (x + 2) + 4<br> O NO<br> O Yes
    14·1 answer
  • 5(x - 1) and 5x - 1<br>is it equivalent ​
    11·2 answers
  • (PLEASE HELP)<br> Find the area of the given trapezoid.
    5·1 answer
  • The two figures are congruent. Find the values of the unknown variables.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!