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Diano4ka-milaya [45]
3 years ago
6

A machining operation produces bearings with diameters that are normally distributed with mean 3.0005 inches and standard deviat

ion .0010 inch. Specifications require the bearing diameters to lie in the interval 3.000±.0020 inches. Those outside the interval are considered scrap and must be remachined. With the existing machine setting, what fraction of total production will be scrap?
Mathematics
1 answer:
padilas [110]3 years ago
7 0

Answer:

5%

Step-by-step explanation:

The 68-95-99.7 rule for the Normal distribution is an empirical rule that remind us the percentages of data that falls between the mean ± 1, ± 2 and ± 3 standard deviations.

That is to say, if the mean is m and the standard deviation s, roughly speaking 68% of the data falls between  [m-s, m+s], 95% between [m-2s, m+2s] and 99.7% between [m-3s, m+3s].

Since the mean is 3.0005 and the standard deviation is s=0.0010, 2s=0.0020, 95% of the data should fall between [3.0005-0.0020, 3.0005+0.0020] and 5% outside this interval. So <em>around 5% of total production will be scrap</em>.

 

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Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to
attashe74 [19]

Answer:

a) Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

b) X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c) t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

p_v =P(t_{(49)}>2.81)=0.0035  

d) If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation  

\bar X=32.12 represent the sample mean  

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =30.2 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c. Perform the test and calculate P-value

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

Since is a one right tailed test the p value would be:  

p_v =P(t_{(49)}>2.81)=0.0035  

d. State your conclusion.

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

6 0
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alexandr402 [8]

Answers:

first term = 37

second term = 46

third term = 55

fourth term = 64

==========================================

Explanation:

Start at 37. Add 9 to this term to get the second term. Add 9 to that result to get the next term, and so on.

first term = 37

second term = 37+9 = 46

third term = 46+9 = 55

fourth term = 55+9 = 64

-----------

The nth term formula is

a(n) = 9n+28

It can be found by plugging a = 37 and d = 9 into the general form

a(n) = a + d*(n-1)

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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