A long history of testing water samples in a certain lake has shown that the level of a certain pollutant is approximately normally
distributed with standard deviation 4.5 mg/L. What is the minimum number of samples required to estimate today's level to within 0.4
mg/L with 95% confidence? (Don't forget to round Zc to two decimal places!)

Answers

Answer 1

Answer:

The minimum number of samples required is 487.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation 4.5 mg/L.

This means that [tex]\sigma = 4.5[/tex]

What is the minimum number of samples required to estimate today's level to within 0.4 mg/L with 95% confidence?

This is n for which M = 0.4. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.4 = 1.96\frac{4.5}{\sqrt{n}}[/tex]

[tex]0.4\sqrt{n} = 1.96*4.5[/tex]

[tex]\sqrt{n} = \frac{1.96*4.5}{0.4}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*4.5}{0.4})^2[/tex]

[tex]n = 486.2[/tex]

Rounding up

The minimum number of samples required is 487.

Related Questions

PLEASE HELP
BRAINLIEST
NO FILE HOSTING LINKS!!
Answer each part. If necessary, round your answers to the nearest hundredth.

Answers

Answer:

a) 11/7 pages or about 1.57

b) 23/11 dollars or 2.09090909....... (goes on forever)

BRAINLIEST PLS

the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

Answers

Answer:

The price per gallon of gas with a $7 car wash is $3.19

Then if you purchase x gallons of gas and also pay for the car wash, the total cost is:

C(x) = $7 + $3.19*x

In the case that you do not pay for the car wash, the cost per gallon is $3.39

Then the cost for x gallons of gas in this case is:

K(x) = $3.39*x

When is it worth it to buy the car wash?

We need to sett the equations:

C(x) = K(x)

This means that you pay exactly the same in both cases, but in one ( C(x)) you get the car wash and in the other not.

Then we need to solve:

$7 + $3.19*x = $3.39*x

$7 = ($3.39 - $3.19)*x = $0.20*x

$7/$0.20 = x = 35

Then for 35 gallons, is worth to buy the car wash.

In the case where the car wash costs $2, then the equation C(x) becomes:

C(x) = $2 + $3.19*x

Then if we solve the same equation:

C(x) =K(x)

$2 + $3.19*x = $3.39*x

$2 = ($3.39 - $3.19)*x

$2 = $0.20*x

$2/$0.20 = x

10 = x

Then for 10 galons is whort buy the car wash.

What are the restrictions on x? square root of 5x^2

Answers

Step-by-step explanation:

there are actually no restrictions. even with a negative x, squaring it makes for a positive result.

Find the distance between the pair of points (2, 3) and (6, 8)

Answers

Answer: d=sqrt(41) =6.4031

Step-by-step explanation:

We know that the distance between the two points (x 1 ,y 1 ) and (x 2 ,y 2 ) is

d= sqrt((x2-x1)^2 +(y2-y1)^2 )

as given

x1=2 ,x2=6 ,y1=3 ,y2=8

d=sqrt((6-2)^2+(8-3)^2 )

d= sqrt((4)^2+(5)^2

d=sqrt(16+25)

d=sqrt(41) =6.4031

Help please due in 45 minutes!!

Answers

Answer:

x=4, y=5

Step-by-step explanation:

Download photo math and take a picture of it

Find the gradient of the line segment between the points (2,3) and (4,7)

Answers

Answer:

1/2

Step-by-step explanation:

take change in X divided by change in Y values

Joseph drove to his grandmother's house which is 279 miles away in 4.5 hours. If he continues at the same speed, approximately how long will it take him to drive 325 miles?

Answers

Answer:

5.24 hours

Step-by-step explanation:

I like to set these up as ratios.

279 miles/4.5 hours = 325 miles/ x hours

Then cross multiply

279x = 4.5 x 325

279x = 1462.5

divide both sides by 279

x = 5.24 hours

You can also solve 279 miles/4.5 hours to get the miles per hour driven, then divide 325 by that number:

279/4.5 = 62mph

325/62 = 5.24

I already know the answer but ima check and see.

Answers

I got 2.29 is the difference and debras cows made more obviously

Fraction form is 229/100

MARK ME BRAINLIEST PLEASE

Find the lateral area of a cylinder
whose radius is 5 cm and whose
height is 10 cm.
Round to the nearest whole number.
[? ] cm2

Answers

Answer:

314 cm^2

Step-by-step explanation:

(=^w^=)

A= 2*pi*r*h

A=2*pi*5*10

A=314.16 cm^2

Step-by-step explanation:

2×5×10=

10×10= 100 cm²

=100 cm²

Find the missing angle. Find x

Answers

Answer: 20

Reason: They're opposite meaning they are the same when compared to the side

PLEASE HELP IMMEDIATELY!!

Answers

Answer:

}

Step-by-step e.xplanati:kljkjk

How to simplify this expression?

(12^15+12^30-12^49)/(-12^28+12^47-(144^6)/12)

Express the answer as 12^?.

Hint: You have to factor 12^? from the top or bottom so that the expression becomes x/(12^?)(x) or (12^?)(x)/x. Then the x should cancel out, and you get 12^? as the answer.

Thanks!!

Answers

Answer:

Not sure if this is what you want the question is worded weirdly.

someone help me please like mega pleaseee help a girl out

Answers

Answer:

≈ $9164.35

Step-by-step explanation:

The future amount A is calculated as

A = P [tex](1+\frac{r}{n}) ^{nt}[/tex]

P is the Principle

r is interest rate

n is number of times per year compounding happens

t is the number of years

Here P = 15000 , r = 16% = 0.16, n = 12 , t = 3

A = 15000 [tex](1+\frac{0.16}{12}) ^{(12(3))}[/tex]

= 15000 ([tex](1.01333)^{36}[/tex]

≈ 24164.35

Interest paid = $24164.35 - $15000 = $9164.35

Answer:

The future amount A is calculated as

A = P (1+\frac{r}{n}) ^{nt}(1+nr)nt

P is the Principle

r is interest rate

n is number of times per year compounding happens

t is the number of years

15 PTS!!! HELP IMMEATLEY
Aaron is designing a party game in which he needs exactly 24 possible outcomes. Which sets of actions can he use to have a statistically fair game?

Randomly select an odd digit {1, 3, 5, 7, 9}, then flip a coin twice.

Randomly select a number from 1 to 16, then roll an 8-sided number cube with the digits 1 to 8.

Spin this and roll an 8-sided number cube with the digits 1 to 8.
Select a card from a set of cards with the letters A through N, then spin this once.
Select a card from a set of cards with the letters A through D, then spin this once.
Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.

Answers

Answer:

Select a card from a set of cards with the letters A through D, then spin this once.

Spin this and roll an 8-sided number cube with the digits 1 to 8.

Y = 5x + 2
6y = 18x + 12
What is the value of X?

Answer:

The distance is 185 between the points (-7,3) and (4,-5)

Step-by-step explanation:

Answer:

Hi! The answer to your question is [tex]\sqrt{185}[/tex]

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

I NEED HELP ASAP HELP HELP HELP....
According to the line plot, what is the total amount of time spent studying by the students who studied for 1/2 of an hour each?

Answers

Answer:

2.5hrs

Step-by-step explanation:

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