Please help to solve this question

A simple random sample of 90 analog circuits is obtained at random from an ongoing production process in which 25% of all circui

kozerog [31]

Answer:

76.10% probability that between 19 and 28 circuits in the sample are defective

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 90, p = 0.25$

So

$\mu = E(X) = np = 90*0.25 = 22.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{90*0.25*0.75} = 4.11$

P(19 ≤ X ≤ 28)

Using continuity correction, this is $P(19-0.5 \leq X \leq 28+0.5) = P(18.5 \leq X \leq 28.5)$ , which is the pvalue of Z when X = 28.5 subtracted by the pvalue of Z when X = 18.5. So

X = 28.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{28.5 - 22.5}{4.11}$

$Z = 1.46$

$Z = 1.46$ has a pvalue of 0.9279

X = 18.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{18.5 - 22.5}{4.11}$

$Z = -0.97$

$Z = -0.97$ has a pvalue of 0.1669

0.9279 - 0.1669 = 0.7610

76.10% probability that between 19 and 28 circuits in the sample are defective

8 0

3 years ago

What is the inverse of the function f(x) =1/9x + 2?

Fittoniya [83]

f(x) = 1/9x + 2

To find the inverse, we need to do this:

Replace f(x) with y

y = 1/9x + 2

Replace x with y

x = 1/9y + 2

Solve for y

Subtract 2

x - 2 = 1/9y

Multiply by 9

9x - 18 = y

Replace y with f^-1(x)

f^-1(x) = 9x - 18

5 0

3 years ago

A film maker wants to make and sell DVDs of a documentary film. It costs $6500 to make the film and $1500 to set up production

algol [13]

Step-by-step explanation:

Cost to make the film : $6500

Cost to set up production: $1500

Additional cost to make each video : $4

Additional cost to make n videos : $4n

total cost to make n videos = $6500 + $1500 + $4n = (8000 + 4n) dollars

overall cost to make each video

= total cost to make n videos ÷ n videos

= (8000 + 4n) / n

by definition, in order to "break even", the selling price for each video must be equal to the cost to make each video. i.e

Price, P(n) = (8000 + 4n) / n

Hence,

P(500) = [8000 + 4 (500)] / 500 = (8000 + 2000) / 500 = $20

This means that in order to break even selling 500 DVD's he has to sell each one for $20

6 0

3 years ago

The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 1/5 ampere when t

Margaret [11]

Answer:

0.102048 ampere

Step-by-step explanation:

I α k / R

Current = 1/5 ; R = 8750

What is the current when the resistance is 17150 ohms

First obtain the value of k :

I = k/R

I = 1/5 ampere = 0.2 A

0.2 = k / 8750

k = 1750

What is the current when the resistance is 17150 ohms

I = 1750 / 17150

I = 0.1020408

I = 0.102048 ampere

8 0

3 years ago

What is the general equation of a tilted ellipses not centered at the origin?

ICE Princess25 [194]

The general equation of an ellipse in which case it is not centered at the origin and it is tilted is; (x-h)²/a² + (y-k)²/b² = 1.

<h3>What is the general equation of a tilted ellipses not centered at the origin?</h3>

It follows from the task content that the plane shape in discuss is an ellipse which is described by the characteristics that it is tilted and not centered at the origin.

It follows from convention that the general equation of such an ellipse is;

(x-h)²/a² + (y-k)²/b² = 1.

In which case, such an ellipse has center given as point; (h, k).