The percent equivalent of 1.09 is ________ and the fraction is _____________

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 X = 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 - α)% 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 z-confidence interval.

The critical value of z 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 z-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 z-interval or t-interval.

If the sample selected is small and the standard deviation is estimated from the sample, then a t-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 n = 10 compute a 95% confidence interval for the temperature as follows:

The (1 - α)% t-confidence interval is:

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

The critical value of t is:

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

*Use a t-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

Escribe un decimal que sea 1/10 de 3.0

Alex777 [14]

Un decimal que es 1/10 de 3,0 es 0,3

8 0

4 years ago

jason is 6 years older than his sister. Their mother is 15 years older than the sum of their ages. If their mother is 39, how ol

zhuklara [117]

Answer:

Jason would be 18 years old

Step-by-step explanation:

sister = 6

mother = 39

mother is 15 year older than the sum of the kids ages

39-15= 24

24-6= 18

Jason is 18 years old

3 0

3 years ago

Write a slope intercept equation for a line passing through the point (4,-2) that is parallel to the line 4x+5y=7. Then write a

LuckyWell [14K]

First, the equation needs to be put into slope-intercept form, which is y = -4/5x + 7/5. Then, you need to know what parallel and perpendicular lines are. REMEBER, parallel lines have the same slope, and perpendicular lines have slopes whose product equal -1. You just need to substitute. For the parallel line, -2 = -4/5(4) + b, and b = 6/5, so y = -4/5x + 6/5. For the perpendicular line, the slope is 5/4. Now substitute. -2 = 5/4(4) + b, and b = -7, so y = 5/4x -7.

3 0

4 years ago

There are 4 sports stores,9 clothing stores and 6 jewelry stores ina shopping crnter which ratio compares the number of sports s

Pani-rosa [81]

The ratio is 2 : 9

Step-by-step explanation:

Given:

The number of sports store = 4

The number of clothing store = 9

The number of jewellery stores = 5

To Find :

The ratio of number of sports stores to the total number of stores

Solution:

The ratio of number of sports stores to the total number of stores

= $\frac{\text{number of sports store}}{\text{ Total number of stores}}$

The total number of stores = number of sports store + number of clothing store + number of jewellery store

The total number of stores = 4 + 9 + 5

The total number of stores = 18

Now the ratio is

= $\frac{4}{18}$ or 4 : 8

The ratio after reduction is

= $\frac{2}{9}$ or 2 : 9 or 2 to 9

7 0

4 years ago

The percent equivalent of 1.09 is ________ and the fraction is ______________

The percent equivalent of 1.09 is and the fraction is ______