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

yaroslaw [1]

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:

$E(X) = 10(0.9) = 9$

3 0

3 years ago

Select all of the ordered pairs that make the inequality y > x2 + 3x – 4 true. (0, 0) (2, 1) (–2, –1) (–5, –1)

fredd [130]

The correct answers are:
___________________________________________________
[A]: " (0, 0) " ; AND:
___________________________________________________
[C]: " (-2, -1) " .
___________________________________________________

Explanation:
___________________________________________________

[A]: " (0, 0) " ; is correct;

Since, when "x = 0" and y = 0 :

"0 > - 4 " ; which is correct.
___________________________________________________
[B]: "(2, 1)" is incorrect, since:

when "x = 2" and "y = 1" ;

" 1 > 6" ; is incorrect.
___________________________________________________
[C]: "(-2, -1)" ; is correct;

Since, when "x = -2" and y = -1" ; then:

"-2 > -6 ; which is correct.
___________________________________________________
[D]: " (-5, -1) " ; is INCORRECT.

since when "x = -5" and "y = -1 ;

then: -1 > 6 ; which is INCORRECT.
___________________________________________________

8 0

3 years ago

What are the coordinates of the midpoint between the points (-4, -9) and (-8, -5)? Select the best answer from the choices provi

OLga [1]

B). (-6,-7)

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

8 0

2 years ago

during a trip to the supermarket, Jim bought the following items bread $1.45 beans $0.88 toothpaste $2.90 milk $3.55 dog food $6

mr Goodwill [35]

15.28 I think it is the answer bc it said total so u add all the numbers. I added them and it gave me 15.28

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3 years ago

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Which of the following are solutions to the equation below (5x+1)^2=7? Check all that apply.

stiv31 [10]

(5x+1)² = 7; expand: 25x² + 10x +1 = 7 or 25x² + 10x -6 = 0

Solve this quadratic for x:

x = [-b + √(b² - 4ac)]/2a and x = [-b - √(b² - 4ac)]/2a
Plug the values and you'll find :
x = (- √7 - 1)/5 (answer C)
x = (+√7 -1)/5 (answer E)

4 0

3 years ago

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