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julia-pushkina [17]

3 years ago

7

Each container holds 1L 275ml of water. How much water is in 609 identical containers? Find the difference between your estimate

d product and precise product.

1 answer:

yan [13]3 years ago

7 0

Do the conversion of 1l to ml and add 275 plus that number then multiply

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The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The

Mademuasel [1]

Answer:

(a) The 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b) The confidence level is 68%.

(c) The necessary assumption is that the population is normally distributed.

(d) The 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

Step-by-step explanation:

Let <em>X</em> = temperature of a certain solution.

The estimated mean temperature is, $\bar x=37^{o}C$ .

The estimated standard deviation is, $s=0.1^{o}C$ .

(a)

The general form of a (1 - <em>α</em>)% confidence interval is:

$CI=SS\pm CV\times SD$

Here,

SS = sample statistic

CV = critical value

SD = standard deviation

It is provided that a large number of independent measurements are taken to estimate the mean and standard deviation.

Since the sample size is large use a <em>z</em>-confidence interval.

The critical value of <em>z</em> for 95% confidence interval is:

$z_{0.025}=1.96$

Compute the confidence interval as follows:

$CI=SS\pm CV\times SD\\=37\pm 1.96\times 0.1\\=37\pm0.196\\=(36.804, 37.196)\\\approx (36.80^{o}C, 37.20^{o}C)$

Thus, the 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b)

The confidence interval is, 37 ± 0.1°C.

Comparing the confidence interval with the general form:

$37\pm 0.1=SS\pm CV\times SD$

The critical value is,

CV = 1

Compute the value of P (-1 < Z < 1) as follows:

$P(-1$

The percentage of <em>z</em>-distribution between -1 and 1 is, 68%.

Thus, the confidence level is 68%.

(c)

The confidence interval for population mean can be constructed using either the <em>z</em>-interval or <em>t</em>-interval.

If the sample selected is small and the standard deviation is estimated from the sample, then a <em>t</em>-interval will be used to construct the confidence interval.

But this will be possible only if we assume that the population from which the sample is selected is Normally distributed.

Thus, the necessary assumption is that the population is normally distributed.

(d)

For <em>n</em> = 10 compute a 95% confidence interval for the temperature as follows:

The (1 - <em>α</em>)% <em>t</em>-confidence interval is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The critical value of <em>t</em> is:

$t_{\alpha/2, (n-1)}=t_{0.025, 9}=2.262$

*Use a <em>t</em>-table for the critical value.

The 95% confidence interval is:

$CI=37\pm 2.262\times \frac{0.1}{\sqrt{10}}\\=37\pm 0.072\\=(36.928, 37.072)\\\approx (36.93^{o}C, 37.07^{o}C)$

Thus, the 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

3 0

3 years ago

Rachel is collecting donations for the local animal shelter. So far she has collected , which is of what she hopes to collect. H

Rudiy27

Answer:

The money Rachael plan to collect for the shelter is <u>$345</u>.

Step-by-step explanation:

<u><em>There are some data missing in the question, so below is the complete question:</em></u>

Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to collect. How much money does Rachel plan to collect for the shelter?

Now, to find the money Rachael plan to collect for the shelter.

Let the total money Rachael plan to collect be $x.$

The amount far she has collected = $245.

Percentage of amount she hopes to collect = 70%.

Now, to get the total money Rachael plan to collect:

$70\%\ of\ x=245$

$\frac{70}{100} \times x=245$

$0.70x=245$

<em>Dividing both sides by 0.70 we get:</em>

$x=\$345.$

Therefore, the money Rachael plan to collect for the shelter is $345.

8 0

3 years ago

I don’t know what the answer to this question is , help

ipn [44]

Answer:

(4, 0)

Step-by-step explanation:

given the 2 equations

y = x - 4 → (1)

- 4x - 6y = - 16 → (2)

substitute y = x - 4 into (2)

- 4x - 6(x - 4) = - 16

- 4x - 6x + 24 = - 16

- 10x + 24 = - 16 ( subtract 24 from both sides )

- 10x = - 40 ( divide both sides by - 10 )

x = 4

substitute x = 4 into (1) for corresponding value of y

y = 4 - 4 = 0

solution is (4, 0)

3 0

3 years ago

There are 12 boys and 16 girls in Marco's class (including Marco). What is the probability that a student chosen at random from

qaws [65]

Answer: 3/7

Step-by-step explanation:

There's 28 student total.

12/28 simplify to 3/7

3 0

3 years ago

The scale for a scale drawing is 8 millimeters: 1 centimeter. Which is larger,the actual object or the scale drawing? PLEASE PLE

Daniel [21]

The centimeter is bigger

5 0

3 years ago