a circle with the radius of 1 cm sits inside a 11cm by 12cm rectangle.What is the area of the shaded region?

Answer: useing the distributive property the method is 4x+8=20

using the reciprocal the method is x+2=5

Step-by-step explanation:

Answer:

Using this method, the equivalent equation is 4x+8=20.

Another method is to use the reciprocal.

Using this method, the equivalent equation is x+2=5.

Step-by-step explanation:

IT IS CORRECT

Answer:

a) [tex]0.81-2.62\frac{0.34}{\sqrt{110}}=0.725[/tex]    

[tex]0.81+2.62\frac{0.34}{\sqrt{110}}=0.895[/tex]    

So on this case the 99% confidence interval would be given by (0.725;0.895)    

b) [tex]n=(\frac{2.58(0.34)}{0.1})^2 =76.95 \approx 77[/tex]

So the answer for this case would be n=77 rounded up to the nearest integer

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=0.81[/tex] represent the sample mean

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

s=0.34 represent the sample standard deviation

n=110 represent the sample size  

Part a

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

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

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=110-1=109[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,119)".And we see that [tex]t_{\alpha/2}=2.62[/tex]

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

[tex]0.81-2.62\frac{0.34}{\sqrt{110}}=0.725[/tex]    

[tex]0.81+2.62\frac{0.34}{\sqrt{110}}=0.895[/tex]    

So on this case the 99% confidence interval would be given by (0.725;0.895)    

Part b

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigmas}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

We can assume the following estimator for the population deviation [tex]\hat \sigma =s =0.34[/tex]

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got [tex]z_{\alpha/2}=2.58/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(0.34)}{0.1})^2 =76.95 \approx 77[/tex]

So the answer for this case would be n=77 rounded up to the nearest integer

Answer:

0.01% probability that the mean ticket price exceeds $33

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 normally distributed samples are 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.

In this problem, we have that:

[tex]\mu = 29.89, \sigma = 5.28, n = 40, s = \frac{5.28}{\sqrt{40}} = 0.8348[/tex]

Find the probability that the mean ticket price exceeds $33

This is 1 subtracted by the pvalue of Z when X = 33. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{33 - 29.89}{0.8348}[/tex]

[tex]Z = 3.73[/tex]

[tex]Z = 3.73[/tex] has a pvalue of 0.9999

1 - 0.9999 = 0.0001

0.01% probability that the mean ticket price exceeds $33

Answer:

[tex]P(\bar X >33)[/tex]

And we can use the z score formula given by:

[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 33 we got:

[tex] z = \frac{33-29.89}{\frac{5.28}{\sqrt{40}}}= 3.725[/tex]

And we can use the complement rule and we got:

[tex] P(Z>3.725)= 1-P(Z<3.725)= 1-0.9999= 0.0001[/tex]

Step-by-step explanation:

Previous conepts

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".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

We know the following properties for the variable of interest:

[tex]\mu = 29.89 , \sigma=5.28 [/tex]

We select a sample size of n = 40>30. From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And for this case we want to find this probability:

[tex]P(\bar X >33)[/tex]

And we can use the z score formula given by:

[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 33 we got:

[tex] z = \frac{33-29.89}{\frac{5.28}{\sqrt{40}}}= 3.725[/tex]

And we can use the complement rule and we got:

[tex] P(Z>3.725)= 1-P(Z<3.725)= 1-0.9999= 0.0001[/tex]

Answer:

U shape

Step-by-step explanation: look for a U shape and youll have chosen a quadratic function but find the vertex and put them into the format then find the slope

3/ 4+2/ 5=1 3/ 20

3 forths + 2 fifths = 1 and 3 twentyiths

Hope i helped! :)

Answer:

.25 or 1/4

Step-by-step explanation:

1/3-1/12 is .25 or if you turn it into a fraction it is 1/4.Because one quarter out of a dollar equals .25 cents.

Answer:

  9 = 1 + 2n

Step-by-step explanation:

A sum is indicated with a plus sign (+). Two times a number is represented by the product of 2 and the variable used to represent the number. Here, we have chosen "n" (for "number"). Then the sum is ...

  1 + 2n

"Is" in this context means "equals", so we have ...

  9 = 1 + 2n

Answer: The accident proportion differ between the two age groups is 0.11.

Step-by-step explanation:

Since we have given that

Number of clients under 18 years of age = 500

Number of clients had had an accident = 180

Proportion of client had an accident = [tex]\dfrac{180}{500}=\dfrac{18}{50}[/tex]

Number of clients aged 18 and older = 600

Number of clients had had an accident = 150

Proportion of client had an accident = [tex]\dfrac{150}{600}=\dfrac{15}{60}[/tex]

So, According to question, we get that

Difference between the two age groups proportions would be :

[tex]\dfrac{18}{50}-\dfrac{15}{60}\\\\=\dfrac{108-75}{300}\\\\=\dfrac{33}{300}\\\\=\dfrac{11}{100}[/tex]

Hence, the accident proportion differ between the two age groups is 0.11.

To find the sample mean greater than 95% of possible sample means for a population mean of 3.25 and standard deviation of 1.75 with a sample size of 300, apply the Central Limit Theorem to calculate the standard error and use the 95th percentile z-score to compute the desired sample mean.

To find the sample mean that is greater than exactly 95% of possible sample means given a population mean (μ) of 3.25 and a standard deviation (σ) of 1.75 for a sample size (n) of 300, we use the concept of a z-score in conjunction with the Central Limit Theorem.

The Central Limit Theorem states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough. Since we have a large sample size of 300, we can assume normality. The formula for the standard error of the mean (SEM) is given by σ divided by the square root of n, SEM = σ / √n. In this case, SEM would be 1.75 / √300.

To find the specific sample mean that would exceed 95% of the sample means, we need to find the z-score that corresponds to the 95th percentile, which is typically around 1.645 for a one-tailed test (since we're looking for means greater than a value). We then multiply this z-score by the SEM and add it to the population mean. The calculation is as follows:

By carrying out these calculations, we will obtain the sample mean that is greater than 95% of possible sample means.

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The sample mean that would be greater than exactly 95% of possible sample means is approximately 3.4164.

Given that the population mean [tex](\(\mu\))[/tex] is 3.25 and the population standard deviation [tex](\(\sigma\))[/tex] is 1.75, we can use the z-score formula to find the sample mean [tex](\(\bar{x}\))[/tex] that corresponds to the 95th percentile:

[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]

We know that for a standard normal distribution, the z-score that corresponds to the 95th percentile is approximately 1.645 (since we want the value that is greater than exactly 95%, we use the one-tailed z-score). We can rearrange the formula to solve for [tex]\(\bar{x}\)[/tex]:

[tex]\[ \bar{x} = \mu + (z \times \frac{\sigma}{\sqrt{n}}) \][/tex]

Now we plug in the values:

[tex]\[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{\sqrt{300}}) \] \[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{\sqrt{300}}) \] \[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{17.3205080756888}) \] \[ \bar{x} = 3.25 + (1.645 \times 0.1010101010101) \] \[ \bar{x} = 3.25 + 0.16641664166417 \] \[ \bar{x} = 3.4164166416642 \][/tex]

Answer:

c

Step-by-step explanation:

a circle with circumference 18 had an arc with 120 central angle. what is the length of the arc

To find the length of a 120-degree arc in a circle with an 18-unit circumference, we apply the fraction of a full circle the angle represents to the total circumference, resulting in an arc length of 6 units.

To determine the length of an arc with a 120-degree central angle in a circle with an 18-unit circumference, we use the relationship between the angle and the circumference of the circle. By knowing that the circumference corresponds to 360 degrees, we can calculate the length of the arc for any given angle by finding what fraction of 360 degrees the angle represents and applying that fraction to the total circumference.

The formula to use is: Arc length (s) = (Angle in degrees/360) * Circumference of the circle. For an angle of 120 degrees, this becomes: s = (120/360) * 18. Doing the math, we find that s = (1/3) * 18, which simplifies to s = 6. Therefore, the length of the arc is 6 units.

Answer:

500 tablets is what you give

Final answer:

To provide a daily dose of 600 mg of calcium carbonate with 400 mg tablets, we need to administer 2 tablets because the calculation of 600 mg divided by 400 mg per tablet equals 1.5, and we round up to the next whole tablet.

Explanation:

If a calcium carbonate supplement is ordered at a dose of 600 mg daily, and the available form is 400 mg tablets, we need to determine how many tablets to administer. To calculate this, we divide the total daily dose required by the dosage available per tablet. Therefore, 600 mg / 400 mg/tablet equals 1.5 tablets. Since we cannot give half a tablet, we round up to the next whole tablet, as it is important not to under-dose a medication.

We get:
600 mg / 400 mg per tablet = 1.5 tablets
Thus, we need to administer 2 tablets to achieve the required daily dose of 600 mg.

Answer:

89.44% probability that the total weight of the King Salmons caught is greater than 575 lbs

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 normally distributed samples are 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.

For sums of size n from a population, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]\sigma\sqrt{n}[/tex]

The weight of the King Salmons are i.i.d. ∼ Normal with µK = 150 lbs and σK = 10 lbs. 4 king salmons.

So [tex]\mu = 4*150 = 600, \sigma = 10\sqrt{4} = 20[/tex]

What is the probability that the total weight of the King Salmons caught is greater than 575 lbs?

This is 1 subtracted by the pvalue of Z when X = 575. So

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

[tex]Z = \frac{575 - 600}{20}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a pvalue of 0.1056

1 - 0.1056 = 0.8944

89.44% probability that the total weight of the King Salmons caught is greater than 575 lbs

Answer:

3/2y * -5

Step-by-step explanation:

-1/2 * -3y= 3/2

-1/2* 10 = -5

Answer and Step-by-step explanation:

We can easily add up these two numbers:

    1,563,001

+     253,965

___________

    1,816,966

Now, we need to write out the answer is words:

"One million, eight hundred sixteen thousand, nine hundred and sixty-six"

Hope this helps!

Answer:

Step-by-step explanation:

1,563,001

+ 253,965

___________

1,816,966

In words:

"One million Eight Hundred Sixteen Thousan Nine hundred and. Sixty Six"

Answer: C. Taking the square root of both sides of the equation.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i got it right

Answer:

The scale doesn't start at 0. One could argue the maximum value should be 7, but this is a formatting choice.

Step-by-step explanation:

Answer:

The scale doesn't start at 0. One could argue the maximum value should be 7, but this is a formatting choice.

Step-by-step explanation:

Answer: −420x+1073

Step-by-step explanation:

Let's simplify step-by-step.

955−105x(4)+118=955+−420x+118

Combine Like Terms:

=955+−420x+118=(−420x)+(955+118)=−420x+1073

Answer: =−420x+1073

I did it on my calculator and it got 653. The calculator is never wrong.

Answer:

22%

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

There are two ways to solve this

a fast way: 125/2400 which equals approx 0.05208

when you convert this to a percentage it is about 5%

another way is take 2400 has 100% and 125 as x%

so

125/2400 = x/100

cross multiply so

2400x = 12500

then

x= 12500/2400 which simplifies to about

5.208. since this was out of 100 from the start you don't need to convert it to percentage form

Answer:

true

Step-by-step explanation:

Answer:

P = -0.004Q + 149

Step-by-step explanation:

The general form of the linear equation is:

[tex]P=aQ+b[/tex]

The slope of the equation (a) can be found by using the two given points (4,000; $133) and (27,000; $41)

[tex]a = \frac{\$41-\$133}{27,000-4,000}\\a=-0.004[/tex]

Applying the point (4,000; $133) to the equation below yields in the linear equation for Price as a function of the number of shirts:

[tex]P-P_0=a(Q-Q_0)\\P-133=-0.004(Q-4,000)\\P = -0.004Q+149[/tex]

The linear equation is:

P = -0.004Q + 149

Answer:

(a) The point estimate for the population proportion p is 0.34.

(b) The margin of error for the 99% confidence interval of population proportion p is 0.055.

(c) The 99% confidence interval of population proportion p is (0.285, 0.395).

Step-by-step explanation:

A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean [tex]\bar x[/tex] is a point estimate of the population mean μ.

Similarly, the the point estimate of the population proportion of a characteristic, p is the sample proportion [tex]\hat p[/tex].

The (1 - α)% confidence interval for the population proportion p is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The margin of error for this interval is:

[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The information provided is:

[tex]\hat p=0.34\\n=500\\(1-\alpha)\%=99\%[/tex]

(a)

Compute the point estimate for the population proportion p as follows:

Point estimate of p = [tex]\hat p[/tex] = 0.34

Thus, the point estimate for the population proportion p is 0.34.

(b)

The critical value of z for 99% confidence level is:

[tex]z={\alpha/2}=z_{0.01/2}=z_{0.005}=2.58[/tex]

*Use a z-table for the value.

Compute the margin of error for the 99% confidence interval of population proportion p as follows:

[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

          [tex]=2.58\sqrt{\frac{0.34(1-0.34)}{500}}[/tex]

          [tex]=2.58\times 0.0212\\=0.055[/tex]

Thus, the margin of error for the 99% confidence interval of population proportion p is 0.055.

(c)

Compute the 99% confidence interval of population proportion p as follows:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

[tex]CI=\hat p\pm MOE[/tex]

     [tex]=0.34\pm 0.055\\=(0.285, 0.395)[/tex]

Thus, the 99% confidence interval of population proportion p is (0.285, 0.395).

The point estimate for p is 0.34. The margin of error, calculated using a z-score of 2.576, is 0.034. The 99% confidence interval is from 0.306 to 0.374.

This question is about calculating a confidence interval for a proportion using the normal distribution. The best point estimate for p is the sample proportion, p-hat, which is 0.34.

For a 99% confidence interval, we use a z-score of 2.576, which corresponds to the 99% confidence level in a standard normal distribution. The formula for the margin of error (E) is: E = Z * sqrt[(p-hat(1 - p-hat))/n]. Substituting into the formula, E = 2.576 * sqrt[(0.34(1 - 0.34))/500] = 0.034.

The 99% confidence interval for p is calculated by subtracting and adding the margin of error from the point estimate: (p-hat - E, p-hat + E). The 99% confidence interval is (0.34 - 0.034, 0.34 + 0.034) = (0.306, 0.374).

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Answer:

0.0625 gallons per mile

Step-by-step explanation:

Answer:

87 green apples

Step-by-step explanation:

Red apples  : green apples = 2 : 3

Number of red apples = 2x

Number of green apples = 3x

Total apples = 145

3x + 2x = 145

5x = 145

x = 145/5

x = 29

Number of green apples = 3x = 3 * 29 = 87

Answer:

you have to include how much the cd is worth first

Step-by-step explanation:

you would do

cd price x 1.6 (to the power of 10)

Answer:

The Normal curve with the mean and standard deviations is shown below.

Step-by-step explanation:

According to the Empirical Rule in a normal distribution with mean µ and standard-deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:

The length of the thorax in a population of male fruit flies is approximately Normal.

The mean is, µ = 0.800 mm and the standard deviation is, σ = 0.078 mm.

Then:

The Normal curve with the mean and standard deviations is shown below.

Answer:

21 maybe?

Step-by-step explanation:

if those numbers represent lengths and those lines are the same size, x is 21

Answer:

Statement A - True.

Statement B - False.

Statement C - True.

Statement D - False.

Step-by-step explanation:

(a) A sequence is convergent if and only if all of its subsequences are convergent - this statement is correct.

(b) A sequence is bounded if and only if all of its subsequences are bounded - this statement is incorrect.

(c) A sequence is monotonic if and only if all of its subsequences are monotonic - this statement is correct.

(d) A sequence is divergent if and only if all of its subsequences are divergent - this statement is incorrect.

Final answer:

In the context of mathematical sequences, statements (a), (b), and (c) regarding convergence, boundedness, and monotonicity are true as all subsequences follow the property of the original sequence. However, statement (d) is false because even divergent sequences can have convergent subsequences.

Explanation:

When analyzing the behavior of sequences and series in mathematics, it's important to understand various characteristics such as convergence, boundedness, monotonicity, and divergence. We can assess the truthfulness of the given statements based on these characteristics.

Assessment of the Statements:

(a) True: A sequence is convergent if and only if all of its subsequences are convergent. This is a fundamental property of convergent sequences, implying that if the original sequence approaches a specific value, every subsequence will also approach that same value.

(b) True: A sequence is bounded if and only if all of its subsequences are bounded. Every subsequence of a bounded sequence also has to be bounded, because it cannot exceed the bounds set by the original sequence.

(c) True: A sequence is monotonic if and only if all of its subsequences are monotonic. Regardless of which elements are chosen to form a subsequence, if the original sequence preserves its direction of progression (either increasing or decreasing), so will the subsequences.

(d) False: A sequence is divergent if and only if all of its subsequences are divergent. Here we have a counterexample: consider the sequence (-1)ⁿ, which diverges. However, it has convergent subsequences, such as the constant subsequences of all 1s or all -1s.

Therefore, statements (a), (b), and (c) are true, while statement (d) is false. Understanding the conditions for convergence, boundedness, and monotonicity is key to studying the behaviors of sequences and leveraging properties like the comparison test for evaluating whether a series converges or diverges.

Answer:

a.

[tex]\text{Sample Space} = \{ CCC,CCW,CWW,WWW,WWC,WCC,WCW,CWC \}[/tex]

b.

(i)  1/2

(ii) 2/3

(iii) 1/6

Step-by-step explanation:

a.

The sample space is the list of all possibilities.

[tex]\text{Sample Space} = \{ CCC,CCW,CWW,WWW,WWC,WCC,WCW,CWC \}[/tex]

b.

(i)

If exactly one answer is correct the favorable outcomes are

CWW , WCW , WWC.

And the probability would be 3/6 = 1/2.

(ii)

If at least two answers are correct then the favorable outcomes are

CCC,CCW,WCC,CWC

and the probability is 4/6 = 2/3.

(iii)

If  no answer is correct, the favorable outcomes are

WWW

and the probability is  1/6.

Answer:

24

Step-by-step explanation:

because you need to multiply 6x4x3 divided by 3

Answer:

Bb 24in2

Step-by-step explanation:

It is correct

correct on E D G E N U I T Y

Answer:

[tex]Z = 1[/tex]

Step-by-step explanation:

Z - score

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.

In this problem, we have that:

[tex]\mu = 61, \sigma = 4[/tex]

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

This is Z when X = 65. So

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

[tex]Z = \frac{65 - 61}{4}[/tex]

[tex]Z = 1[/tex]