Peter is the owner of a hardware supply shop. He has hired you to check his machines calibration prior to starting production on a large order. To check this, you set the machine to create 2.0 inch nails and manufacture a random sample of 200 nails. That sample of nails has an average length of 2.024 inches with a standard deviation of 0.205 inches.


Does this sample provide convincing evidence that the machine is working properly or should it be shut down for repairs?

Answer:

The standard deviation is $13,052.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When the head of the household has a college degree, the mean before-tax family income is $ 85,050.

This means that [tex]\mu = 85,050[/tex]

Suppose that 56% of the before-tax family incomes when the head of the household has a college degree are between $75,000 and $95,100 and that these incomes are normally distributed.

They are equally as far from the mean, one above, and one below. This means that when [tex]X = 95100[/tex], Z has a pvalue of 0.5 + (0.56/2) = 0.78. So when X = 95100, Z = 0.77. We use this to find [tex]\sigma[/tex].

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.77 = \frac{95100 - 85050}{\sigma}[/tex]

[tex]0.77\sigma = 10050[/tex]

[tex]\sigma = \frac{10050}{0.77}[/tex]

[tex]\sigma = 13052[/tex]

The standard deviation is $13,052.

Answer:

19x - 25

steps:

(8x + 11x) + (-7 - 18)

19x + (-25)

positive x negative = negative

19x - 25

Answer:

19x - 25

Step-by-step explanation:

(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...

19x + (-7 - 18) <--------------- subtract the bold ones...

(19x) - 25 <-------------------- eliminate parenthases

19x - 25 <--------------------- solution...

73

Step-by-step explanation:

I think that this is an isosceles triangle, and like since ST=SR

Therefore, m(<T) = m(<R)= 73

The estimated proportion of all shoppers who were happy with their experience that day and said yes is 0.667.

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

A store owner asks each person to write "Yes" or "No" on a slip of paper as they leave, secretly writing down whether they were happy with their experience.

At the end of the day, the owner selects 12 slips at random and looks at them. These were the results:

To estimate the proportion is the following formula:

[tex]p'=\dfrac{x}{n}[/tex]

Here, x is the number of success and n is the sample size. Here, the sample size is 12 and number of success (yes) is 8. Thus, the estimated proportion is:

[tex]p'=\dfrac{8}{12}\\p'=0.667[/tex]

Thus, the estimated proportion of all shoppers who were happy with their experience that day and said yes is 0.667.

Learn more about the random sample here;

https://brainly.com/question/17831271

#SPJ1

Answer:

Step-by-step explanation:

(A) não tenho sertesa

Answer:

3. y = -⅕x - 5

Step-by-step explanation:

The equation of straight line is given by the formula, y = mx + c

Where;

m is the slope.

x and y are the points.

c is the intercept.

Given the standard form equation;

x + 5y = -25

Rearranging the equation, we have;

5y = -x - 25

Dividing all through by 5, we have;

y = -⅕x - 5

Answer:

Step-by-step explanation:

27 ÷ 90 = 0.3 = 0.30 = 30%

Answer:

a) [tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]

b) The 95th percentile is 4.4935 hours.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours.

This means that [tex]\mu = 4, \sigma = 1.2[/tex]

16 reviews.

This means that [tex]n = 16, s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]

A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.

This is the pvalue of Z when X = 4.25 subtracted by the pvalue of Z when X = 3.5. So

X = 4.25

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{4.25 - 4}{0.3}[/tex]

[tex]Z = 0.83[/tex]

[tex]Z = 0.83[/tex] has a pvalue of 0.7967

X = 3.5

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3.5 - 4}{0.3}[/tex]

[tex]Z = -1.67[/tex]

[tex]Z = -1.67[/tex] has a pvalue of 0.0475

0.7967 - 0.0475 = 0.7492

So

[tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]

C. Find the 95th percentile for the mean time to complete one month's reviews.

This is X when Z has a pvalue of 0.95, so X when Z = 1.645.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]1.645 = \frac{X - 4}{0.3}[/tex]

[tex]X - 4 = 0.3*1.645[/tex]

[tex]X = 4.4935[/tex]

The 95th percentile is 4.4935 hours.

Answer:

Step-by-zbastep explanation:

Answer:

x is form

Step-by-step explanation:

Answer:

D = 6.32

Step-by-step explanation:

-2 to -4 = 2

-3 to 3 = 6

D² = 2² + 6²

D² = 4 + 36 = 40

D = 6.32

Answer:

x2 - 9x +20

Step-by-step explanation:

Answer:

6.1

Step-by-step explanation:

area =leanth x breath.

if one side=4.7,

then, missing length=area/given side

= 28.67/4.7

=6.1

Answer:

a=81.0

there ya go

Answer:

m<W: 23

Step-by-step explanation:

8x - 9 + 30x - 4 + 13x - 11 = 180

51x - 24 = 180

51x = 204

x = 4

m<W:

8x - 9

8(4) - 9

32 - 9

23

Step-by-step explanation:

I think your answer will be 15

Answer:

960 sq cm

Step-by-step explanation:

(16*12*10)/2

Answer:

a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb

b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of ​35 lb.

This means that [tex]\mu = 160, \sigma = 35[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{35}{\sqrt{10}} = 11.07[/tex]

a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.​

This is 1 subtracted by the pvalue of Z when X = 158. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{158 - 160}{11.07}[/tex]

[tex]Z = -0.18[/tex]

[tex]Z = -0.18[/tex] has a pvalue of 0.4286

1 - 0.4286 = 0.5714

0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.

b.) Does this elevator appear to be​ safe?

No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.

Answer:

Sales tax = $1.25

Total = $25+$1.25 = $26.25

Step-by-step explanation:

Tax = 0.05 x 25 = 1.25

Total = 1.25 + 25

Answer:

To calculate tip or tax, simply move the decimal place 2 to the right and multiply it by the price. For example, If you want to leave a 20% tip, multiply the cost by 0.20 to get the tip amount or multiply the cost by 1.20 to get the total

The sales tax is $1.25

The total price is $26.25

Answer:

coefficient because they are not the same so they can not be constant because it is not the same in every week

Answer:

The probability percentage that both players will be seniors is 15.38%.

Step-by-step explanation:

Given that a football team has 5 freshman, 8 sophomores, 11 juniors, and 16 seniors, if two are chosen at random to participate in the coin toss, to determine what is the probability that both players chosen will be seniors the following calculation must be done:

5 + 8 + 11 + 16 = 40

16/40 = X

4/10 = X

0.4 = X

15/39 = X

5/13 = X

0.38 = X

0.4 x 0.38 = X

0.1538 = X

Thus, the probability percentage that both players will be seniors is 15.38%.

Answer:

a. Fred's margin of error is larger than Ted's.

Step-by-step explanation:

Margin of error of a confidence interval:

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

In which z is related to the confidence level(the higher the confidence level the larger the value of z) [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

From this, we have that:

A higher confidence level leads to a larger margin of error.

A larger sample size leads to a smaller margin of error.

In this question:

Same confidence level.

Fred's sample is smaller, so his margin of error will be larger.

The correct answer is given by option a.

For the same confidence level, Fred's sample is smaller, so hir margin of error will be larger. The correct option is A.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

Fred and Ted are interested in the average height of NC State students.

They randomly sample students from NC State and construct confidence intervals from their data.

Fred sampled 121 students to construct his confidence interval.

Ted sampled 144 students to construct his confidence interval.

The margin of error of a confidence interval

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

Where z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation level and n is a sample size.

By the formula, we have

A higher confidence level leads to a larger margin of error.

A larger sample size leads to a small margin of error.

For the same confidence level, Fred's sample is smaller, so hir margin of error will be larger. The correct option is A.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

6.95

Step-by-step explanation:

to find how much stephanie spends for first we will find how much probhjot spends and then subtract 3.45 dollars from that value alvin spends 2.60 dollars

prohbjot spends 4 times as much as alvin or

4× 2.60=10.4

so prohbjot spends 10.4 dollars

stephanie spends3.45 dollars less than prohbjot or

10.4 -3.45 =6.95

so stephanie spends 6.95 dollars

Answer:

Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.