What is the answer ?

Answer:

1.15

Step-by-step explanation:

The required constant of proportionality of equation P = 1.15 n is k = 1.15.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The equation for the price of the kiwis is,

P = 1.15 n

Here, P, shows the price and n shows the number of kiwis.

The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality.

Let a proportionality equation is,

y = k x,

k is the constant of proportionality here,

To find the constant of proportionality,

Compare the given equation P = 1.15 n with standard proportionality equation,

k = 1.15

The constant of proportionality is 1.15 unit.

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Answer:The answer is 8x10^7

Step-by-step explanationi took the thing

Answer:

The sampling distribution of the sample mean is:

[tex]\bar X\sim N(\mu_{\bar x}=2.4,\ \sigma_{\bar x}=0.40)[/tex]

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

Let X = number of cars running a red light in a day, at a given intersection.

The information provided is:

[tex]E(X)=\mu=2.4\\SD(X)=\sigma=4\\n=100[/tex]

The sample selected is quite large, i.e. n = 100 > 30.

The Central limit theorem can be used to approximate the sampling distribution of the sample mean number of cars running a red light in a day, by the Normal distribution.

The mean of the sampling distribution of the sample mean is:

[tex]\mu_{\bar x}=\mu=2.4[/tex]

The standard deviation of the sampling distribution of the sample mean is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{4}{\sqrt{100}}=0.40[/tex]

The sampling distribution of the sample mean is:

[tex]\bar X\sim N(\mu_{\bar x}=2.4,\ \sigma_{\bar x}=0.40)[/tex]

Final answer:

The sampling distribution of the sample mean is approximately normally distributed, with a mean of 2.4 cars and a standard deviation of 0.4 cars.

Explanation:

The sampling distribution of the sample mean can be described as follows:

Answer:

Step-by-step explanation:

1/8

1/2 multiply 1/4

Answer:

x = -7

Step-by-step explanation:

2x + 3 = x - 4

→ Minus x from both sides to isolate -4

x + 3 = -4

→ Minus 3 from both sides to isolate x and henceforth find the value of x

x = -7

Answer:

We can select a lower confidence level and increase the sample size.

Step-by-step explanation:

The precision of the confidence interval depends on the margin of error ME = Zcritical * Sqrt[(p(1-p)/n]

In this Zcritical value is in the numerator. Z critical decreases as Confidence level decreases. (Zc for 99% = 2.576, Zc for 95% is 1.96, Zc for 90% = 1.645). Therefore decreasing the Confidence level decreases ME.

Also we see that sample size n is in the denominator. So the ME decreases as sample size increases.

Therefore, We can select a lower confidence level and increase the sample size.

The best option that could be used to produce higher precision in our estimates of the population proportion is;

Option C; We can select a lower confidence level and increase the sample size.

Formula for confidence interval is given as;

CI = p^ ± z√(p^(1 - p^)/n)

Where;

p^ is the sample proportion

z is the critical value at given confidence level

n is the sample size

Now, the margin of error from the CI formula is:

MOE = z√(p^(1 - p^)/n)

Now, the lesser the margin of error, the narrower the confidence interval and thus the more precise is the estimate of the population proportion.

Now, looking at the formula for MOE, two things that could change aside the proportion is;

z and n.

Now, the possible values of z are;

At CL of 99%; z = 2.576

At CL of 95%; z = 1.96

At CL of 90%; z = 1.645

We can see that the higher the confidence level, the higher the critical value and Invariably the higher the MOE.

Thus, to have a narrow CI, we need to use a lower value of CL and increase the sample size.

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Answer:

8.8 ounces

Step-by-step explanation:

3.96/0.45=8.8

Answer:

(a)25 Milligrams

(b)15%

(c)[tex]A(10) = 25(0.85)^{10}[/tex]

Step-by-step explanation:

The amount in milligrams of a drug in the body t hours after taking a pill is given by the model:

[tex]A(t) = 25(0.85)^t[/tex]

(a)Comparing this with the exponential decay model, [tex]A(t)=A_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }[/tex], the initial dose given is 25 milligrams.

(b)From the model,

[tex]A(t) = 25(0.85)^t\\A(t) = 25(1-0.15)^t[/tex]

We can also use this method:

[tex]r = a - 1 = 0.85 - 1 = -0.15=-15\%[/tex]

We can see that for every hour, 15% of the drug leaves the body.

(c)After 10 hours

When t=10

[tex]A(10) = 25(0.85)^{10}[/tex]

The amount of drug left after 10 hours is given above in function notation.

a. The initial dose given is 25 milligrams. b. 85(0.85)^t percent of the drug leaves the body each hour. c. The amount of drug left after 10 hours is 0.2147 milligrams.

a. The initial dose given can be found by substituting t = 0 into the function A(t) = 25(0.85)^t. This gives A(0) = 25(0.85)^0 = 25(1) = 25 milligrams.

b. To find the percent of the drug that leaves the body each hour, we need to find the rate of change of A(t) with respect to time. Taking the derivative of A(t) gives dA/dt = 25(0.85)^t * ln(0.85) = 21.25(0.85)^t. This represents the rate of change of A(t) with respect to time. To find the percent, we can divide this rate by the initial dose and multiply by 100: (21.25(0.85)^t / 25) * 100 = 85(0.85)^t percent.

c. To find the amount of drug left after 10 hours, we substitute t = 10 into the function A(t) = 25(0.85)^t: A(10) = 25(0.85)^10 = 25(0.0859) = 0.2147 milligrams.

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Answer:

the answer is 13!

Step-by-step explanation:

hope this helps

Answer:

the answer is 13

Step-by-step explanation:

Answer:

Yes, it is convincing evidence to conclude that the proportion of red cars that drive too fast on this

highway is greater than the proportion of non-red cars that drive too fast.

Step-by-step explanation:

From the, we wish to first test;

H0; P_r - P_o = 0

And; H0; P_r - P_o > 0

Where; P_r and P_o are the proportion of red cars and other cars, respectively, who are driving too fast.

We will use a significance level of a = 0.05.

Thus;

The procedure is a two-sample z-test for the difference of proportions.

For, Random Conditions: The policemen chose cars randomly by rolling a die.

10%: We can safely assume that the number of cars driving past the rest area is essentially infinite, so the 10% restriction does not apply.

Large counts: The number of successes and failures in the two groups are 18, 10, 75, and 130—all of which are at least 10.

So, P_r = 18/28 = 0.64

P_o = 75/205 = 0.37

P_c = (18 + 75)/(28 + 205) = 0.4

Thus:

z = [(0.64 - 0.37) - 0]/√[[(0.4 x 0.6)/28] + [(0.4 x 0.6)/205]]

z = 2.73

From the one tailed z-score calculator online, I got P value = 0.003167

Thus, the P-value of 0.0032 is less than a = 0.05, so we reject H0. We

have sufficient evidence to conclude that the proportion of red cars that drive too fast on this

highway is greater than the proportion of non-red cars that drive too fast.

Answer:

The numbers are 16 and 7

Step-by-step explanation:

Let the numbers be x and y

x+y = 23

x-y = 9

Add the two equations together

x+y = 23

x-y = 9

-------------------

2x = 32

Divide each side by 2

2x/2 = 32/2

x = 16

Now subtract the two equations

x+y = 23

-x +y = -9

-------------------

2y = 14

Divide by 2

2y/2 = 14/2

y = 7

Final answer:

The two numbers with a sum of 23 and a difference of 9 are 16 and 7. Solved by setting up equations for the sum and difference, then solving for the two unknowns.

Explanation:

To find the two numbers with a sum of 23 and a difference of 9, we can set up two equations based on the given information:

Adding the two equations together, we get:

2x = 32

Dividing both sides by 2:

x = 16

Now, substituting x back into one of the original equations, for example, x + y = 23:

16 + y = 23

y = 23 - 16

y = 7

Therefore, the two numbers are 16 and 7.

Job A is the correct answer! :)

Based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.

The factors that should determine if a job should be accepted or not include:

                                          Job A          Job B            Job C

Salary                              $46,650     $38,750       $52,880

Benefits                             14,000        15,000           8,000

Average monthly rent          850             790               950

Annual rent                    $10,200       $9,480         $11,400 ($950 x 12)

Earnings before tax     $50,400     $44,270       $49,480

Thus, based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.

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Answer:

dS/dt ≈ 0.0343

Step-by-step explanation:

We are given;

C = 1.32 x 10^(5)

R = 1.3 x 10^(-2)

dR/dt = 1.0 x 10^(-5)

The function is: S = C(R² - r²)

We want to find dS/dt when r is constant.

Thus, let's differentiate since we have dR/dt;

dS/dR = 2CR

So, dS = 2CR.dR

Let's accommodate dt. Thus, divide both sides by dt to obtain;

dS/dt = 2CR•dR/dt

Plugging in the relevant values to get;

dS/dt = 2(1.32 x 10^(5))x 1.3 x 10^(-2) x 1.0 x 10^(-5)

dS/dt = 3.432 x 10^(-2)

dS/dt ≈ 0.0343

Answer:

243

Step-by-step explanation:

3x3=9

9x3=27

27x3=81

81x3=243

Answer:

[tex] \epsilon = Y -X\beta[/tex]

And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:

[tex] Cov (\epsilon) = \sigma^2 I[/tex]

So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:

The regression model assumes the errors are normally distributed.

Step-by-step explanation:

Assuming that we have n observations from a dependent variable Y , given by [tex] Y_1, Y_2,....,Y_n[/tex]

And for each observation of Y we have an independent variable X, given by [tex] X_1, X_2,...,X_n[/tex]

We can write a linear model on this way:

[tex] Y = X \beta +\epsilon [/tex]

Where [tex]\epsilon_{nx1}[/tex] i a matrix for the error random variables, and for this case we can find the error ter like this:

[tex] \epsilon = Y -X\beta[/tex]

And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:

[tex] Cov (\epsilon) = \sigma^2 I[/tex]

So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:

The regression model assumes the errors are normally distributed.

Final answer:

The best statement is that the regression model assumes the errors are normally distributed. In regression analysis, it is essential that the errors are independent, normally distributed, and have constant variance, which supports the validity of the model's predictions.

Explanation:

The correct statement among the provided options is that the regression model assumes the errors are normally distributed. This is a fundamental assumption of linear regression analysis, where it's assumed that the residuals or errors of the regression model are randomly distributed about an average of zero. These error terms must be independent, normal, and have constant variance (homoscedasticity) across all levels of the independent variables.

According to the theoretical foundation of regression, it is not assumed that errors have an increasing mean, nor that they have zero variance, as some diversity in errors is expected. Additionally, the assumption that errors are indeed dependent would violate the principles of ordinary least squares (OLS) regression, making the model invalid.

Normality, independence, and equal variance are key premises in regression analysis to ensure the validity of the model's inferences. Indeterminate errors that affect the dependent variable 'y' are assumed to be normally distributed and independent of the independent variable 'x'. This maintains the integrity of the regression model.

Answer:

86.96

Step-by-step explanation:

not sure what is height or base.

Answer:

86.96

Step-by-step explanation:

Answer:

2nd, 4th and last one are correct answers

Step-by-step explanation:

[tex] {16}^{ \frac{5}{2} } \\ = ( {4}^{2} )^{ \frac{5}{2} } \\ = {4}^{{2} \times \frac{5}{2} } \\ = {4}^{5} \\ [/tex]

Options: 2nd, 4th and last one are correct answers

Answer:

100,000 lol

Step-by-step explanation:

Answer:

y = x+1

Step-by-step explanation:

You should use the point-slope form of y-y1 = m(x-x1) to solve this.

First you use the slope formula to find your slope. (y2-y1)/(x2-x1)

(-1 - -3)/(-2 - -4) = 2/2 = 1

With the slope of 1 found, just plug a point into the point-slope form.

y-(-1) = (1)(x-(-2)) ->

y+1 = x+2 ->

y = x+1

y=x+1 is the equation of a line that passes through (-2, -1) and (-4, -3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The slope of line passing through  (-2, -1) and (-4, -3)

m = -3+1/-4+2

=-2/-2= 1

Now let us find y intercept

-1=1(-2)+b

-1=-2+b

b=1

Hence, y=x+1 is the equation of a line that passes through (-2, -1) and (-4, -3)

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Answer:

a) 2.81 b)-2.33 c) -2.88 d)3.09

Step-by-step explanation:

The complete question is:

Determine the value of z so that the area under the standard normal curve

a. in the right tail is 0.025 Round your answer to two decimal places.

b. in the left tail is 0.01 Round your answer to two decimal places.

c. in the left tail is 0.002 Round your answer to two decimal places.

d. in the right tail is 0.01 Round your answer to two decimal places.

a)P( Z> ???)=  0.0025

P(Z> ???)= 1-P(Z<???)

P(Z<???)= 1-0.0025

P(Z<??)= 0.9975

From Z distribution table,

Z = 2.81

b) P(Z<???)= 0.01

From Z distribution table

Z= -2.33

c) P(Z< ??? ) = 0.002

From Z distribution table

Z= -2.88

d) P( Z> ???)=  0.001

P(Z> ???)= 1-P(Z<???)

P(Z<???)= 1-0.001

P(Z<??)= 0.999

From Z distribution table,

Z=3.09

Answer:

[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]

Step-by-step explanation:

[tex]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/tex]

[tex]cos(a+b)[/tex]

We need to expand cos(a+b) using the cos addition formula.

[tex]cos(a+b)=cos(a)cos(b)-sin(a)sin(b)[/tex]

We know that we also need to use Euler's formula for sin, which is:

[tex]sin(x)=\frac{e^{ix}-e^{-ix}}{2}[/tex] (you can get this from a similar way of getting the first result, of simply just expanding [tex]e^{ix}=cosx+isinx[/tex] and seeing the necessary result)

We can now substitute our cos's and sin's for e's

[tex]cos(a+b)=(\frac{e^{ia}+e^{-ia}}{2})(\frac{e^{ib}+e^{-ib}}{2})-(\frac{e^{ia}-e^{-ia}}{2})(\frac{e^{ib}-e^{-ib}}{2})[/tex]

Now lets multiply out both of our terms, I'm using the exponent multiplication identity here ([tex]e^{x+y}=e^xe^y[/tex])

[tex]cos(a+b)=\frac{e^{i(a+b)} + e^{i(a-b)}+e^{i(-a+b)} + e^{i(-a-b)}}{4}-\frac{e^{i(a+b)} - e^{i(a-b)}-e^{i(-a+b)}+e^{i(-a-b)}}{4}[/tex]

Now we can subtract these two terms.

[tex]cos(a+b)=\frac{2e^{i(a-b)}+2e^{i(-a+b)}}{4}[/tex]

This is starting to look a lot tidier, let's cancel the 2

[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]

Using Euler's formula, we can write cos(x) as the average of exp(ix) and exp(-ix). Further, we demonstrated how to express cos(a+b) and cos(a)cos(b) in terms of exponential functions, utilizing the properties of Euler's formula and complex exponentials.

Using Euler's formula, exp(ix) = cos(x) + i sin(x) and exp(-ix) = cos(x) - i sin(x), we can represent cos(x) as a combination of exp(ix) and exp(-ix). By adding these two equations, we eliminate the sin(x) terms due to their opposite signs, leading us to the formula for cos(x):

cos(x) = (exp(ix) + exp(-ix)) / 2

To express cos(a+b), use the expansion:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Using Euler's formula, this expands to:

cos(a+b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2 - [exp(ia) - exp(-ia)]/2i * [exp(ib) - exp(-ib)]/2i

Similarly, to express cos(a)cos(b), we again use the representation of cos(x) in terms of exp:

cos(a)cos(b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2

The anchor drops 63 meters in the first 5 seconds.

The given function E(t) = -2.4t + 75 represents the elevation of the ship's anchor relative to the water's surface at any given time t. To find how far the anchor drops every 5 seconds, substitute t = 5 into the function:

E(5) = -2.4(5) + 75

E(5) = -12 + 75

E(5) = 63

Therefore, after 5 seconds, the anchor has dropped 63 meters relative to the water's surface. This indicates the change in elevation during this time period. The negative coefficient of t in the function implies a downward motion, and the constant term (75) represents the initial height of the anchor above the water. So, the anchor drops 63 meters in the first 5 seconds.

Answer:

We need to conduct a hypothesis in order to check if the mean the actual mean length of movies released during 2010-2015 is more than the data base value (a;ternative hypothesis) ,so then the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 117[/tex]  

Alternative hypothesis:[tex]\mu > 117[/tex]  

Step-by-step explanation:

Data given and notation  

[tex]\bar X=118.44[/tex] represent the sample mean

[tex]s=8.82[/tex] represent the sample standard deviation

[tex]n=160[/tex] sample size  

[tex]\mu_o =117[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean the actual mean length of movies released during 2010-2015 is more than the data base value (a;ternative hypothesis) ,so then the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 117[/tex]  

Alternative hypothesis:[tex]\mu > 117[/tex]  

Answer:

=2p(-2p-5)

Step-by-step explanation:

2p(–3p2 + 4p – 5)

=2p(4p-6p-5)

=2p(-2p-5)

Answer:

Step-by-step explanation:

Sample mean = (14 + 10 + 13 + 10 + 11)/5 = 11.6

Sample standard deviation,s = √(summation(x - mean)/n

Summation(x - mean) = (14 - 11.6)^2 + (10 - 11.6)^2 + (13 - 11.6)^2 + (10 - 11.6)^2 + (11 - 11.6)^2 = 13.2

s = √(13.2/5) = 1.62

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 8.9

For the alternative hypothesis,

µ > 8.9

it is a right tailed test because of >.

Since the number of samples is 5 and no population standard deviation is given, the distribution is a student's t.

Since n = 5,

Degrees of freedom, df = n - 1 = 5 - 1 = 4

t = (x - µ)/(s/√n)

Where

x = sample mean = 11.6

µ = population mean = 8.9

s = samples standard deviation = 1.62

t = (11.6 - 8.9)/(1.62/√5) = 3.73

We would determine the p value using the t test calculator. It becomes

p = 0.01

Since alpha, 0.05 > than the p value, 0.01, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that mean anger score of the marines is greater than that of college men.

Therefore, the marines's negative moods increased and it is higher than that of college men.

Answer:

598

Step-by-step explanation:

Answer:

598

Step-by-step explanation:

[tex]23[14 + 4(36 \div 12)] \\ = 23[14 + 4(3)] \\ = 23[14 + 12] \\ = 23 \times 26 \\ = 598 \\ [/tex]

Answer:

Correct option: (B) 71.89%.

Step-by-step explanation:

R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient of determination.

The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent variable).

The coefficient of determination R² can be computed by the formula,

[tex]R^{2}=\frac{SSR}{SST}[/tex]

Here,

SSR = sum of squares of regression

SST = sum of squares of total

From the output attached below the value of SSR and SST are:

SSR = 37043.3236

SST = 51531.0863

Compute the value of R² as follows:

[tex]R^{2}=\frac{SSR}{SST}[/tex]

     [tex]=\frac{37043.3236 }{51531.0863}[/tex]

     [tex]=0.7188539\\\approx 0.7189[/tex]

Thus, the fraction of the variability in house size is explained by income and size of family is 71.89%.

The correct option is (B).

To find the fraction of the variability in house size that is explained by family income and size, we sum the two SSR values and express this as a fraction or percentage of the total variability in house size. The actual value could not be determined from the provided information as it appears to be missing.

The question focuses on understanding the impact of family income and family size (the independent variables) on the house size (the dependent variable). The builder calculated the Sum of Squares for Regression (SSR) considering each independent variable given other independent variables constant. These calculations provide crucial insights into the contribution made by each independent variable to the variation in the dependent variable.

The total SSR (from both variables) can be calculated by summing the SSRs given: SSR(X1 ∣ X2) = 36400.6326 and SSR(X2 ∣ X1) = 3297.7917, which gives 39698.4243. This total variability is a representation of the entire variability in house size that is accounted for by both family income and family size. Express this as a fraction or percentage of total variability in house size to determine the proportion of variability explained by the two predictors.

Note: The Excel output and the options (A. 84.79%, B. 71.89%, C. 17.56%, D. 70.69%) should contain the exact proportion but in the provided information, these values are missing.

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Answer:

[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]    

[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]    

So on this case the 98% confidence interval would be given by (3.767;4.233)

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".

[tex]\bar X=4[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=1[/tex] represent the population standard deviation

n=100 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that [tex]z_{\alpha/2}=2.326[/tex]

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

[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]    

[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]    

So on this case the 98% confidence interval would be given by (3.767;4.233)

Answer:

The probability that the sample mean would differ from the population mean by greater than 0.8 kg is P=0.3843.

Step-by-step explanation:

We have a population with mean 60 kg and a variance of 100 kg.

We take a sample of n=118 individuals and we want to calculate the probability that the sample mean will differ more than 0.8 from the population mean.

This can be calculated using the properties of the sampling distribution, and calculating the z-score taking into account the sample size.

The sampling distribution mean is equal to the population mean.

[tex]\mu_s=\mu=60[/tex]

The standard deviation of the sampling distribution is equal to:

[tex]\sigma_s=\sigma/\sqrt{n}=\sqrt{100}/\sqrt{118}=10/10.86=0.92[/tex]

We have to calculate the probability P(|Xs|>0.8). The z-scores for this can be calculated as:

[tex]z=(X-\mu_s)/\sigma_s=\pm0.8/0.92=\pm0.87[/tex]

Then, we have:

[tex]P(|X_s|>0.8)=P(|z|>0.87)=2*(P(z>0.87)=2*0.19215=0.3843[/tex]