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2 years ago

Help, very important hw!!!

Mathematics

1 answer:

kvv77 [185]2 years ago

8 0

The stem-and-leaf plot for the distribution is given as follows:

1| 9

2| 2 2 3 5 7 7 8 8

3| 0 1 1 2 3 3 4 5 5 5 7 8 9

4| 0 0 1 3

b) From the plot, the correct options are given as follows:

A typical content is 32 calories per 100 ml.

The distribution is roughly symmetric.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

For this problem, the observations are given at the top in red, and using each first digit as the key, the stem and leaf plot is:

1| 9

2| 2 2 3 5 7 7 8 8

3| 0 1 1 2 3 3 4 5 5 5 7 8 9

4| 0 0 1 3

The mean of these observations is:

(19 + 2 x 22 + 23 + 25 + 2 x 27 + 2 x 28 + 30 + 2 x 31 + 32 + 2 x 33 + 34 + 3 x 35 + 37 + 38 + 39 + 2 x 40 + 41 + 43)/26 = 32(approximately)

The correct statements from the plot are as follows:

A typical content is 32 calories per 100 ml(due to the mean).

The distribution is roughly symmetric(13 values below the mean, 13 at or above).

More can be learned about stem-and-leaf plots at brainly.com/question/28015028

#SPJ1

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24" 4 * 3 = Х I really need help the help with this

GREYUIT [131]

288. 4 times 3 is 12. Multiply that with 24 and thats your answer.

8 0

3 years ago

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

yan [13]

Answer:

"The probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.

Step-by-step explanation:

In this case, the quality control expert takes a sample of batteries. From these batteries, we want to find "the probability that the mean battery life would be greater than 948.8 minutes".

Different concepts needed to take into account to solve this question

Sampling Distribution of the Means

For doing this, we need to use the sampling distribution of the means, which results from taking the mean for each possible sample coming from a random variable $\\ x$ . Roughly speaking, each sample will have a different mean, $\\ \overline{x}$ , and the probability distribution for any of these means is called the sampling distribution of the means.

The sampling distribution of the means has a mean that equals the population's mean for the random variable $\\ x$ , i.e., $\\ \mu$ , and its standard deviation is $\\ \frac{\sigma}{\sqrt{n}}$ . We can express this mathematically as:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

Standardized Values for $\\ \overline{x}$

We can standardized the values for $\\ \overline{x}$ using z-scores:

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

This random variable $\\ Z$ follows a standard normal distribution, that is, $\\ Z \sim N(0,1)$ , and it is easier to find probabilities since the values for them are tabulated in the standard normal table (available in any Statistics book or on the Internet.)

What type of distribution follows the sampling distribution of the means?

A general rule of thumb is that this distribution (the sampling distribution of the means) follows a normal distribution if the sample size, $\\ n$ , is bigger than or equal to 30 observations, or $\\ n \geq 30$ . In this case, $\\ n = 109$ batteries. This is a result from the Central Limit Theorem, fundamental in Statistical Inference.

Standard Deviation

We have to remember that the standard deviation is the square root of the variance $\\ \sigma^2$ , or $\\ \sqrt{\sigma^2}$ .

$\\ \sigma^{2} =5929$
$\\ \sigma = \sqrt{5929} = 77$

Therefore, the standard deviation in this case is $\\ \sigma = 77$ minutes.

In sum, we have the following information to answer this question:

$\\ \sigma = 77$ minutes.
$\\ \mu = 941$ minutes.
$\\ n = 109$ batteries (the sample size is large enough to assume that the sampling distribution of the means follows a normal distribution).
$\\ \overline{x} = 948.8$ minutes.

What is the probability that the mean battery life would be greater than 948.8 minutes?

Well, having all the previous information, we can use [2] to solve this question (without using units):

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{948.8 - 941}{\frac{77}{\sqrt{109}}}$

$\\ z = \frac{7.8}{\frac{77}{\sqrt{109}}}$

$\\ z = \frac{7.8}{7.37526}$

$\\ z = 1.05758 \approx 1.06$

This result is the standardized value or z-score for $\\ \overline{x}$ , considering $\\ \mu = 941$ and $\\ \sigma = 77$ .

We round z to two decimals digits since standard normal table only uses it as an entry to find probabilities.

With $\\ z = 1.06$ , we can consult the cumulative standard normal table. First, we need to find with $\\ z = 1.0$ in the first column in the table. Then, in its first raw, we need to find +0.06. The intersection for these two values determines the cumulative probability for $\\ P(z$ .

It is important to recall that $\\ P(z$ because $\\ z = 1.06$ is the standardized value for $\\ \overline{x} = 948.8$ minutes.

Then, $\\ P(z$

However, the question is about $\\ P(\overline{x} > 948.8) = P(z>1.06)$

And

$\\ P(\overline{x} > 948.8) + P(\overline{x} < 948.8) = 1$

$\\ P(z>1.06) + P(z$

Then

$\\ P(z>1.06) = 1 - P(z$

$\\ P(z>1.06) = 1 - 0.8554$

$\\ P(z>1.06) = 0.1446$

Therefore, "the probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.

6 0

4 years ago

Solve using the substitution method 3x+5 =y. 3= 2y +x The x coordinate is ?

slamgirl [31]

3x+5 =y

3= 2(3x+5) +x
3=6x+10+x
3=7x+10

-7=7x

x=-1 :))

7 0

3 years ago

Read 2 more answers

PLEASE HELP I WILL GIVE BRAINLIEST TO RIGHT ANSWER

tigry1 [53]

1: 19 (4x+25=6x -13, solve for x, 25+13=6x-13, 38=2x, x=19, 4(19)+25=101 6(19)-13+101)

2: 23 (3x-8=2x+15)

3: Madison has $59 and Saul has $31 (together they have $90 so divided by 2 and you get 45, Madison has 6 dollars more so subtract 6 from Saul and ad 6 to Madison, make sure that when you ad them you get $90)

4 : 5 weeks ($3 each week, so you multiply 3x5 and get 15. 15+57=72 but the problem says more then so maybe it’s 6 weeks cause that’s $75)

5: 10 weeks (he has 1,800 and needs 2,150, subtract 1,800 from 2,150 for how much he needs. You get 350. He needs that and he makes 35 a week so that would be 350 divided by 35, which is 10)

6:20 miles (it’s 2.25 for that’s first mile. He spent 6.05 so subtract 2.25 from 6.05 and you get 3.80, 3.80 divided by 0.20 is 19, then you need to add that first mile and it’s 20)

7: 6 figures in a complete set (Charlie starts out with 2 and Patrick starts out with 20 individual figures. Charlie has 6 sets and Patrick has 3, i multiplied the number of sets they had by 6 then added their individual figures until they numbers matched up)

8: an orange has 45 calories and an apple has 75 calories (5x-150=3x, 5x-3x= -2x, -2x divided by -150 = 75, 75-30 is 45. 75 is the apple and because it’s 30 more you subtract 30 for orange)

4 0

3 years ago

Show work for 3,220÷4

snow_lady [41]

That's the answer
do you understand?

8 0

3 years ago