Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48.3 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 40 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 48.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate comp

Answers

Answer 1

Answer:

0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 48.3 ppm and a standard deviation of 8 ppm.

This means that [tex]\mu = 48.3, \sigma = 8[/tex]

Sample of 40:

This means that [tex]n = 40, s = \frac{8}{\sqrt{40}}[/tex]

Find the probability that the disposal of such capacitors will be regulated.

Sample mean above 48.5, which is 1 subtracted by the p-value of Z when X = 48.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{48.5 - 48.3}{\frac{8}{\sqrt{40}}}[/tex]

[tex]Z = 0.16[/tex]

[tex]Z = 0.16[/tex] has a p-value of 0.5636.

1 - 0.5636 = 0.4364

0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.


Related Questions

PLEASE HELP



what's x
cos(x+pi)-sin(x-pi)=0

please show work​

Answers

sin(x+pi)=-sin(x)=sin(-x)=cos(pi/2)

cos (x+pi)=-cos(x)

So according to the question:

cos(pi/2 +x)=cos(x)

Using the solution of cos, obtain:

(pi/2) + x = 2pi +- (x)

case#1: (pi/2) + x = 2pi + (x)

But here, the value of x is canceled, just

case#2: (pi/2) + x = 2pi - (x)

answer------------>>>>>>>>> x=pi-pi/4

Omar, Amare, and Jack paid a total of $68.25 for dinner and tickets to a concert. The concert
tickets cost $9.75 each. If the 3 friends split the dinner bill equally, how much did each friend
spend on dinner?

Answers

Answer:

32.5

Step-by-step explanation:

I I divided ot then added it together

67-2x+89/2+7-8x=0
help me please​

Answers

Answer:

x = 11.85

Step-by-step explanation:

[tex]67 - 2x + \frac{89}{2} + 7 -8x = 0\\\\67 + \frac{89}{2}+7 = 8x + 2x\\\\\frac{134 + 89 +14}{2} = 10x\\\\10x = 118.5\\\\x = 11.85[/tex]

Answer:

[tex]x = 11 \frac{17}{20}[/tex] or [tex]\frac{237}{20}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

What is the vertical shift of this sinusoidal function?
question is in pic pls help asap :)​

Answers

Answer photo math download it

Step-by-step explanation:

has everything

PLS HELP ASAP!! need the answer

Answers

Answer:

60 degrees

Step-by-step explanation:

Find the equation (in terms of x ) of the line through the points (-3,4) and (1,-8)

Answers

Answer:

A(-3,4) B(1,-8)

y-y1/x-x1 =y2-y1/x2-x1

y-4/x--3 = -8-4/1--3

y-4/x+3 = -12/1+3

y-4/x+3 =-12/4

y-4/x+3 = -3

y-4 = -3(x+3)

y-4=-3x-9

y+3x +9-4=

y+3x+5=0

Answer:

y = -3x - 5

Step-by-step explanation:

-3, 4 and 1, -8

1 - -3 = 4

-8 - 4 = -12

[tex]\frac{-12}{4}[/tex] = [tex]\frac{-3}{1}[/tex] = -3

gradient/slope = -3

now substituting in the point -3, 4 to find the y intercept:

4= -3 x -3 + c

4 = 9 + c

-5 = c

y intercept = -5

equation is y = -3x - 5

University of Florida researchers in the Department of Materials Science and Engineering have invented a technique that rapidly detects traces of TNT (Today, Spring 2005). The method, which involves shining a laser on a potentially contaminated object, provides instantaneous results and gives no false positives. In this application, a false positive would occur if the laser detected traces of TNT when, in fact, no TNT were actually present on the object. Let A be the event that the laser light detects traces of TNT. Let B be the event that the object contains no traces of TNT. The probability of a false positive is 0.

Required:
Write this probability in terms of A and B using symbols such as U, ∩ and |.

Answers

Answer:

P(A n B) = 0

Step-by-step explanation:

Given

[tex]A \to[/tex] Traces of TNT detected

[tex]B \to[/tex] No traces of TNT

Required

Probability of false positive

From the question, we understand that A and B must occur to get a positive and the result is 0.

The probability of A and B is represented as: P(A n B)

Include the result (0), we get:

P(A n B) = 0

The expression 4x* represents 144​

Answers

Answer:

x=36

Step-by-step explanation:

because 4x36=144

Answer:

4x = 144

4 • 36 = 144

The answer to the equation is 36

Find the length of side y.
y=_ft

Answers

Answer:

y = 5.66388 feet, (round that to whatever you need to round to)

Step-by-step explanation:

cos (51) = y/9

cos(51)*9=

y = 5.66388 feet


PLS ANSWER RN

What is the area of AJKL?

Answers

Answer:

8.5

Step-by-step explanation:

slope of the line that contains KL

(y2 - y1)/(x2-x1)

(0-1)/(7-3)

m = -1/4

slope of the line that contains JK

(5-1)/(4-3)

m = 4

the linea are perpendicular so triangle is right

area = (leg1 x leg2)/2

KL = [tex]\sqrt{(7-3)^2 + (0-1)^2} = \sqrt{16 + 1} = \sqrt{17}[/tex]

KJ = [tex]\sqrt{(4-3)^2 + (5-1)^2}= \sqrt{1 + 16} = \sqrt{17}[/tex]

area = (√17)^2/2 = 17/2 = 8.5

8.5



….hope this helps!

equations equivalent to x/4+1/3=5/6

Answers

If I rewrite this it would be
3x/12+4/12=10/12
3x=6
So your answer would be
2/4+1/3=5/6
Or
1/2+1/3=5/6
X=2

Find the mean of the following data set: 8.9, 7.2, 3.3, 2.5, 9.4, 3.9, 4.5, 5.4, 8.9

Answers

the mean if the following set is 6

Encuentre el volumen de 35 kg de oro

Answers

Speak in English so that I can understand

In the given figure, which angle is complementary to <4

Answers

Answer: The definition of a complementary angle is "Either of two angles whose sum is 90°." Thus the complementary angle for 4 is angle 5.

P.S. if you feel this answer is satisfactory I would appreciate it if you would mark it brainiest.

If the pattern shown continues, how many black keys appear on a pipe organ with a total of 120 keys? Suggestion: use equivalent ratios or a rate table to rationalize your answer.
HURRYYYYY I NEEDDD HELP

Answers

in 12 key 5 black keys are appearing so consider x key will appear in 120 keys

120/x = 12/5

solving further,

x= 50

Answer - If the pattern shown continues, 50 black keys appear on a pipe organ with a total of 120 keys!

Can someone help me please?

Answers

the answer is 0.62

62/100 = 0.62

Answer:

0.62

Step-by-step explanation:

the 62 is the number you're mainly working with and the 100 represents the place value! so the 100 means you need to place the top number in the hundredths place (0.62)

Hope this helps! Good luck with your math work!

PLEASE HELP IM BEING TIMED

Answers

Answer:

1

Step-by-step explanation:

Any number to the 0 power is equal to 1.

Hope that this helps!

Answer:

1 is correct

Any number that is raised to the power of 0 is 1, and any number that’s raised to the power of 1 is itself

the given tables shows the number of shirts and pants different people own. what number correctly completes the table so that each person has the same ratio of pants to shirts​

Answers

Answer:

He needs 15 shirts

Step-by-step explanation:

We can use a ratio to solve

4 pants             6 pants

--------------- = -------------

10 shirts            x shirts

Using cross products

4x = 10 *6

4x = 60

Divide each side by 4

4x/4 = 60/4

x = 15

He needs 15 shirts

△JKL has vertices at J(−2, 4), K(1, 6), and L(4, 4). Determine whether △JKL is a right triangle

Answers

Answer:

Not a right triangle

Obtuse isosceles triangle.

Sides: J = 3.606   K = 6   L = 3.606

Step-by-step explanation:

hope helps you

have a nice day

Match each tool with how we used it in class

Answers

Answer:

1 - b

2 - a

3 - c

Step-by-step explanation:

1. B
2.a
3.c
Hope this helps

What is the range of y= sec-'(x)? PreCal, send help please!!

Answers

Given:

The function is:

[tex]y=\sec^{-1}(x)[/tex]

To find:

The range of the given function.

Solution:

We have,

[tex]y=\sec^{-1}(x)[/tex]

The range of secant inverse function is:

[tex]Range=\{y|0\leq y\leq \pi , y\neq \dfrac{\pi}{2}\}[/tex]

The range of the given function in interval notation is:

[tex]Range=\left[0,\dfrac{\pi}{2}\right)\text{ and }\left( \dfrac{\pi}{2}, \pi\right ][/tex]

Therefore, the correct option is C.

Dan spent 0.125 of his money in snacks, 1/4 on travelling and saved the
rest. If he saved $65, how much money did he have at first?​

Answers

Answer:

89.38

Step-by-step explanation:

65 times 0.125 = 8.125

65 times 0.25 = 16.25

16.25 plus 8.125 plus 65 = 89.38 dollars

A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 0.7. From the sample, the mean difference was 0.95, with a standard deviation of 0.44. Calculate the test statistic, rounded to two decimal places

Answers

Answer:

The test statistic is t = 3.36.

Step-by-step explanation:

You're testing the claim that the mean difference is greater than 0.7.

At the null hypothesis, we test if it is 0.7 or less, that is:

[tex]H_0: \mu \leq 0.7[/tex]

At the alternate hypothesis, we test if it is greater than 0.7, that is:

[tex]H_1: \mu > 0.7[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that [tex]\mu = 0.7[/tex]

Survey of 35 people. From the sample, the mean difference was 0.95, with a standard deviation of 0.44.

This means that [tex]n = 35, X = 0.95, s = 0.44[/tex]

Calculate the test statistic

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}[/tex]

[tex]t = 3.36[/tex]

The test statistic is t = 3.36.

I only need help on number six

Answers

Answer:

288 inches = 8 yards

Step-by-step explanation:

Answer:

[tex]6 . \: 8 \: yards \: = \: 288 \: inches[/tex]

[tex]8. \: 18 \: feets \: = \: 216 \: inches[/tex]

[tex]10. \: \frac{1}{3} \: yards \: = 12 \: inches[/tex]

Step-by-step explanation:

6. 1 yard = 36 inches

8 yards = 36 × 8

= 288

8. 1 feet = 12 inches

18 feets = 12 × 18

= 216 inches

10. 1/3 into decimal = 0.33333333333

1/3 yards = 0.33333333333 × 36

= 12 inches

Hope it is helpful....

Find the volume of the cone. Round your answer to the nearest hundredth.

Answers

Answer:

I believe the answer is 1.36

Hi plz help, if you can ill mark you 5 starz! :)

Answers

Answer:

12 kg, 1200 mm, 1200 ml (twice), 12 m, and 120 mm

Answer:

12,000 is 12

120 is 120

1.2 L is 1200

1200 is 120

0.12 is 12

Q.6.
Lisa wanted to paint her ugly brown flower box
red. Using the given dimensions, how many square
inches will she have to paint? (remove the top
base)

Answers

Answer:

10x22x8

Step-by-step explanation:

1760 is the answer

Write the inverse function for the function, ƒ(x) =1/2 x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.

ƒ -1(x) =

ƒ -1(4) =

Answers

Answer:

0

Step-by-step explanation:

Given that f(x) = 1/2x + 4

Let y = f(x)

y = 1/2 x + 4

Replace y with x

x = 1/2 y + 4

Make y the subject of the formula

1/2y = x - 4

y = 2(x-4)

If x = 3

y = 2(4-4)

y = 2(0)

y = 0

Hence ƒ -1(4) is 0

The price of an item has been reduced by 70% the original price was $20 what is the price of the item now

Answers

Just find 70 % of $20 and that’s the price.

20 x 0.7 = 14
20 - 14 = 6

The price of the item is $6

What's the answer to this? I thought it was -138 apparently it's not? :(

Answers

The answer is 78 because if you substitute with the x=3 it changes the outcome of the answer:)
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