-6(4y-30) greater than or equal to -102

Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below.

garik1379 [7]

Answer:

The 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =9.2$ represent the sample mean 1

$\bar X_2 =8.8$ represent the sample mean 2

n1=27 represent the sample 1 size

n2=30 represent the sample 2 size

$\sigma_1 =0.3$ population standard deviation for sample 1

$\sigma_2 =0.1$ population standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =9.2-8.8=0.4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$0.4-1.96\sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}=0.281$

$0.4+1.96\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=0.519$

So on this case the 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

6 0

3 years ago

What is the probability that a person who is above 35 years old has a hemoglobin level of 9 or above?

lorasvet [3.4K]

Answer:

Option C. $P=0.531$

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

so

Let

x------> size of the event space (total person's hemoglobin level of 9 or above with age above 35 years)

y-----> size of the sample space (total person's age above 35 years)

so

$P=\frac{x}{y}$

In this problem we have

$y=162$

Complete the table to find the total person's hemoglobin level of 9 or above (person's age above 35)

Let

y------> total person's hemoglobin level between 9 and 11 (person's age above 35)

$y+76+40=162$

$y=46$

Find the value of x

$x=46+40=86$

substitute the values

$P=\frac{86}{162}=0.531$

4 0

3 years ago

Read 2 more answers

What is the answer to <br> 2(6d+3)=18-3(16-3d)

marishachu [46]

Answer:

3

d

=

−

36

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Finding area of a sector

katen-ka-za [31]

The smaller sector is 360-255=105 degree
it is 105/360 portion of the whole circle, and the area of the whole circle is πr², r is 14
so the area of the smaller sector is (105/360)*π*14²
run those numbers through your calculator, use 3.14 for π, you get 179.5

if you are looking for area of the larger sector, it would be
(255/360)*π*14²=435.94

3 0

3 years ago

Math help please FAST

Tasya [4]

Answer:

180

60

40

Step-by-step explanation:

Angles in a triangle add up to equal 90 degrees

Equilateral - has all congruent angles and congruent sides

If a triangle has 3 angles and the angles add up to equal 180 then the measure of one angle in an equilateral = 180 / 3 = 60

Bisect means to split into to equal parts

So if you bisect an 80 degree angles you will have two 40 degree angles. ( Because 80/2 = 40 )

3 0

3 years ago

Read 2 more answers