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
galina1969 [7]
3 years ago
15

Based on past experience, the main printer in a university computer centre is operating properly 90% of the time. Suppose inspec

tions are made at 10 randomly selected times. A) What is the probability that the main printer is operating properly for exactly 9 inspections. B) What is the probability that the main printer is operating properly for at least 3 inspections? C) What is the expected number of inspections in which the main printer is operating properly?
Mathematics
1 answer:
yaroslaw [1]3 years ago
3 0

Answer:

a) 38.74% probability that the main printer is operating properly for exactly 9 inspections.

b) Approximately 100% probability that the main printer is operating properly for at least 3 inspections.

c) The expected number of inspections in which the main printer is operating properly is 9.

Step-by-step explanation:

For each inspection, there are only two possible outcomes. Either it is operating correctly, or it is not. The probability of the printer operating correctly for an inspection is independent of any other inspection, which means that the binomial probability distribution is used 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.

Based on past experience, the main printer in a university computer centre is operating properly 90% of the time.

This means that p = 0.9

Suppose inspections are made at 10 randomly selected times.

This means that n = 10

A) What is the probability that the main printer is operating properly for exactly 9 inspections.

This is P(X = 9). So

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

P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874

38.74% probability that the main printer is operating properly for exactly 9 inspections.

B) What is the probability that the main printer is operating properly for at least 3 inspections?

This is:

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

So

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

P(X = 0) = C_{10,0}.(0.9)^{0}.(0.1)^{10} \approx 0

P(X = 1) = C_{10,1}.(0.9)^{1}.(0.1)^{9} \approx 0

P(X = 2) = C_{10,2}.(0.9)^{2}.(0.1)^{8} \approx 0

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0 = 0

Then:

P(X \geq 3) = 1 - P(X < 3) = 1 - 0 = 1

Approximately 100% probability that the main printer is operating properly for at least 3 inspections.

C) What is the expected number of inspections in which the main printer is operating properly?

The expected value for the binomial distribution is given by:

E(X) = np

In this question:

E(X) = 10(0.9) = 9

You might be interested in
Ebonie invests in $2500 today in an account earning 7%. How much will she have in 5 years?
nikdorinn [45]

Answer:

Amount she Receive in 5 years = $3506.37

Step-by-step explanation:

Given in question as

Ebonie invests amount in account = P = $2500

The interest rate she will have = 7%

The amount will keep in account for 5 years

Now we apply compound interest (CI ) to determine how much she will receive after 5 years ,

So , for CI

Amount = principal ( 1 + \frac{Rate}{100} ^ T     ,where T is Time

So, A = 2500 ( 1 +\frac{7}{100})^5

Or, A = 2500 (1.40255)

Or, A = $3506.37

Hence Amount she will receive $ 3506.37  Answer

3 0
3 years ago
Help im timed The ratio of strawberries to bananas in a smoothie recipe are shown in the graph below.
Dmitriy789 [7]

Answer:

D

Step-by-step explanation:

Match the x and y coordinates with strawberries and bananas.

(6,1)

(12,2)

(18,3)

7 0
2 years ago
Read 2 more answers
Solve for x in the parallelogram below.<br> PLEASE HURRY
Elina [12.6K]

Answer:

x=6

Step-by-step explanation:

Hope it was right

7 0
3 years ago
Read 2 more answers
Pls help I’ll brainlest
Lisa [10]

Answer: You need to show the question for me to answer it. In other words, provide more context

Step-by-step explanation:

7 0
2 years ago
1. There are 3.76 x 10^22 tardigrades in 1gram of water. How many tardigrades are there in 600 grams of water?
vova2212 [387]

Answer:

2.256 x 10^25

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Y+15 &lt;3 for inequality
    7·1 answer
  • a retiree invests $1240 for 3.5 years in a savings plan that pays a simple interest of 2.1% per year. How much interest will be
    9·1 answer
  • A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35
    13·1 answer
  • Write a division problem that the quotient is 5/8
    10·1 answer
  • lucas lives 5/8 mile from school.kenny lives twice as far as lucas from school.how many miles does kenny live from school
    11·1 answer
  • Two lines intersect to form a linear pair with equal measures. One angle has the measure 6x° and the other angle has the measure
    14·1 answer
  • jorge jogged the trail to the waterfall at 120 yard/min and walked back at 80 yards/min if the entire trip took 2 hours, how lon
    8·1 answer
  • Round 1.18769843885 to 5 decimal places
    15·1 answer
  • Help me please please
    6·2 answers
  • Simplify. 15 X plus 2Y plus X plus 7X plus 8Y
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!