In 10-mph crash tests, 25% of a certain type of automobile sustain no visible damage. A modified bumper design has been proposed in an effort to increase this percentage. Let denote the proportion of all cars with this new bumper that sustain no visible damage in 10-mph crash test. The hypothesis to be tested is The test will be based on an experiment involving independent crashes of car prototypes with the new bumper. Let denote the number of crashes resulting in no visible damage, and consider the test procedure that rejects

(a) Find the probability of type I error.

Answer: C. 8.1

I just got that one wrong, but there is the right answer

The diameter of the circle is C. 8.125 inches.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given is a circle.

Given, chord FE is a perpendicular bisector of chord BC.

Here FE is the diameter of the circle.

We have a chord theorem which states that products of the lengths of the segments of line formed by two intersecting chords on each chord are equal.

Let X be the intersecting point of the chords.

Here, using the theorem,

BX . CX = FX . EX

3.5 × 3.5 = 2 × EX

EX = 6.125

Diameter = FE = FX + EX = 2 + 6.125 = 8.125

Hence the diameter is 8.125 inches.

Learn more about Circles here :

https://brainly.com/question/266951

#SPJ7

The complete question is given below.

Answer:

26/9

Step-by-step explanation:

8/9=.88888888888889 (on calc)

2+8/9

18/9+8/9

=26/9

Answer:

b = 28

Step-by-step explanation:

8*21 then 168/6 = 28

Answer:

b = 28

Step-by-step explanation:

[tex] \frac{6}{8} = \frac{21}{b} \\ \\ b = \frac{21 \times 8}{6} \\ \\ b = \frac{7\times 8}{2} \\ \\ b = 7 \times 4 \\ \\ \huge \red{ \boxed{ b = 28}}[/tex]

Answer: -8 is greater than -10

Step-by-step explanation: When in the negatives, the smaller the number, the greater it is

Answer:

Step-by-step explanation:

The correct answer is (B).

Let X = the number of people that are displeased in a random sample of 25 people selected from a population of which 4.5% will be displeased regardless of the situation. Then X is a binomial random variable with n = 25 and p = 0.045.

P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – binomcdf(n: 25, p: 0.045, x-value: 1) = 0.311.

P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 0C25(0.045)0(1 – 0.045)25 – 25C1(0.045)1(1 – 0.045)24 = 0.311.

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem can be solved using the binomial distribution since we have a fixed number of trials (selecting 25 people) and each trial has two possible outcomes (displeased or not displeased).

Let p be the probability of an individual being displeased, which is given as 0.045 (or 4.5% as a decimal).

Then, the probability of an individual not being displeased is:

1 - p = 0.955.

Let X be the number of displeased people in a random sample of 25.

We want to find the probability that at least two people are displeased, which can be expressed as:

P(X ≥ 2) = 1 - P(X < 2)

To calculate P(X < 2), we can use the binomial distribution formula:

[tex]P(X = k) = (^n C_k) \times p^k \times (1 - p)^{n-k}[/tex]

where n is the sample size (25), k is the number of displeased people, and (n choose k) is the binomial coefficient which represents the number of ways to choose k items from a set of n items.

For k = 0, we have:

[tex]P(X = 0) = (^{25}C_ 0) \times 0.045^0 \times 0.955^{25}[/tex]

≈ 0.378

For k = 1, we have:

[tex]P(X = 1) = (^{25}C_1) \times 0.045^1 \times 0.955^{24}[/tex]

≈ 0.42

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.798.

Finally, we can calculate,

P(X ≥ 2) = 1 - P(X < 2)

= 1 - 0.798

= 0.202.

Thus,

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ2

Answer:

[tex]5\sqrt{3} - 4[/tex]

Step-by-step explanation:

[tex]\sqrt{(4-5\sqrt{3} )^{2} }[/tex]

[tex]5\sqrt{3} - 4[/tex]

Answer:

The distance across the lake from A to B = 690.7 ft

Step-by-step explanation:

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that

∠CAB=46.5∘. He also measures CA as 312 ft and CB as 527 ft. Find the distance between A and B.

Given

A = 46.5°

a = 527 ft

b = 312 ft

To find; c = ?

Using the sine rule

[a/sin A] = [b/sin B] = [c/sin C]

We first obtain angle B, that is, ∠ABC

[a/sin A] = [b/sin B]

[527/sin 46.5°] = [312/sin B]

sin B = 0.4294

B = 25.43°

Note that: The sum of angles in a triangle = 180°

A + B + C = 180°

46.5° + 25.43° + C = 108.07°

C = 108.07°

We then solve for c now,

[b/sin B] = [c/sin C]

[312/sin 25.43°] = [c/sin 108.07°]

c = 690.745 ft

Hope this Helps!!!

To find the distance across the lake from A to B, use trigonometry and the length of side AC and angle CAB to find the length of side AB.

To find the distance across the lake from point A to point B, we can use trigonometry.

Given that ∠CAB = 46.5°, we can find the distance across the lake by finding the length of side AB in triangle CAB.

Since we know the length of side AC (53 m) and the angle CAB (46.5°), we can use the sine function to find side AB:

AB = AC * sin(CAB) = 53 m * sin(46.5°) = 39.6 m

Therefore, the distance across the lake from point A to point B is approximately 39.6 meters.

https://brainly.com/question/15387096

#SPJ11

Answer:

I believe the correct statements are 1), 2), and 3).

The statements provided in the question are all true. The sphere has a radius of 4 cm (A), the diameter's length is twice the length of the radius (B), and the volume of the sphere is 256/3 π cm³ (C).

A) The sphere has a diameter of 8 cm, which is the distance between two points on the surface of the sphere passing through its center. By definition, the diameter is twice the length of the radius. Thus, to find the radius of the sphere, we divide the diameter by 2:

Radius = Diameter / 2

Radius = 8 cm / 2

Radius = 4 cm

B) This statement is true. As mentioned earlier, the diameter of the sphere (8 cm) is indeed twice the length of its radius (4 cm).

C) The volume of a sphere can be calculated using the formula:

Volume = (4/3) * π * Radius³

Now, let's calculate the volume using the given radius:

Volume = (4/3) * π * (4 cm)³

Volume = (4/3) * π * 64 cm³

Volume = 256/3 * π cm³

Hence the correct option is (a), (b) and (c).

To know more about diameter here

https://brainly.com/question/32968193

#SPJ2

Complete Question:

A sphere has a diameter of 8 cm.

A) The sphere has a radius of 4 cm.

B) The diameter’s length is twice the length of the radius.

C) The volume of the sphere is 256/3 π cm³

Answer:

The answer is C (3.5)(0.25)

Step-by-step explanation:

Because to find the area of a rectangle you multiply the base times the height . The formula looks like this.

A=bh

Answer:

Answer Is (3.5)(0.25)

Step-by-step explanation:

Because You'll Need To Multiply The Length,3.5,And The Width,0.25, To Find The Area Of This Rectangle.

Answer:

47

Step-by-step explanation:

x is games won

y is hats sold

[tex]y=3.75x+13.75\\y=3.75(9) + 13.75\\y=47.5[/tex]

Since you can't sell .5 of a hat- you need to round this answer.

Answer:

48

Step-by-step explanation:

2/3 of 1 is simply 2/3 or 0.667

Decimal:0.273 or 0.273273273

Fraction:273/999=91/333

Answer:

0.273 as a fraction is 273/1000

0.273273273... as a repeating decimal, (273/999) as repeating decimal fraction.

Answer:

-7/2

Step-by-step explanation:

[tex]slope = \frac{ - 4 - 10}{7 - 3} \\ \hspace{24 pt} = \frac{ - 14}{4} \\ \hspace{24 pt}= - \frac{7}{2} \\ \huge{ \red{ \boxed{\therefore \: slope = - \frac{7}{2} }}}[/tex]

Answer:

49.5 square feet.

Step-by-step explanation:

6 by 7.5 means 6 x 7.5.

6 x 7.5 = 45

She wants to by 10% extra.

45 is 100% so multiply 45 by 1.1.

45 x 1.1 = 49.5

Olivia's room area is 45 square feet. Considering a 10% extra for waste, she should buy 49.5 square feet of carpet.

To calculate how much carpet Olivia should buy including waste, we first need to figure out the area of her room. The area of a rectangle is found by multiplying the length by the width, so in this case, we multiply 6 feet by 7.5 feet, which equals 45 square feet. Then we factor in the 10 percent extra for waste - which is 4.5 square feet (10% of 45). Adding these together, we get a total of 49.5 square feet. Therefore, Olivia should buy 49.5 square feet of carpet. The correct answer is B. 49.5 square feet.

https://brainly.com/question/329987

#SPJ11

Answer:

Step-by-step explanation:

X = cost of PB  

Y = cost of J

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Dividing everything in the first equation by 2:

3X + 2Y =  966 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Elimination method... let's multiply the first equation by 3 and the second equation by -2.

   9X +   6Y =   2898

-10X + -6Y  = -3134

-X = -236

X =  236 --> so the price of the PB is 236 pennies or $2.36

Plugging into the second equation as the numbers are a bit smaller,

5X + 3Y = 1567

5(236) + 3Y = 1567

1180 + 3Y = 1567

3Y = 387

Y = 129. So the price of the jelly is 129 pennies or $1.29.

Now we check:  4 x $1.29 + 6*2.36 = $19.32

                       3 x $1.29 + 5 x 2.36 = $15.37

The answers are verified and highlighted in bold.

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

By setting up a system of equations to represent the cost of the items bought by Erin and Adam, you can solve to find the cost of the 'j' (jelly) and 'p' (peanut butter). It's similar to solving a problem to find the cost of different fruits in a fruit basket.

We can solve this problem using algebra, particularly the system of linear equations. Let's denote 'j' as the cost of a jar of jelly and 'p' as the cost of a jar of peanut butter. We will use the information given in the question to set up two equations:

For Erin's purchases, it is 4j + 6p = $19.32. For Adam's purchases, it is 3j + 5p = $15.67.

Now, you can solve this system of equations using the substitution or elimination method, and find the cost of the jar of peanut butter and jelly.

Notice that this example is similar to finding the cost of fruit when we know the total price and the number bought, like in the fruit basket example provided earlier. This is an example of solving for unknowns using algebraic equations.

https://brainly.com/question/31653301

#SPJ11

Answer:

95% confidence interval for the population variance of the number of tissues per box is [5043.11 , 23401.31].

Step-by-step explanation:

We are given that a consumer magazine counts the number of tissues per box in a random sample of 15 boxes of No- Rasp facial tissues. The sample standard deviation of the number of tissues per box is 97.

Firstly, the pivotal quantity for 95% confidence interval for the population variance is given by;

                         P.Q. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2}__n_-_1[/tex]

where, [tex]s^{2}[/tex]  = sample variance = [tex]97^{2}[/tex] = 9409

              n = sample of boxes = 15

           [tex]\sigma^{2}[/tex]  = population variance

Here for constructing 95% confidence interval we have used chi-square test statistics.

So, 95% confidence interval for the population variance, [tex]\sigma^{2}[/tex] is ;

P(5.629 < [tex]\chi^{2}__1_4[/tex] < 26.12) = 0.95  {As the critical value of chi-square at 14

                                         degree of freedom are 5.629 & 26.12}  

P(5.629 < [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] < 26.12) = 0.95

P( [tex]\frac{5.629 }{(n-1)s^{2} }[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{26.12 }{(n-1)s^{2} }[/tex] ) = 0.95

P( [tex]\frac{(n-1)s^{2} }{26.12 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1)s^{2} }{5.629 }[/tex] ) = 0.95

95% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1)s^{2} }{26.12 }[/tex] , [tex]\frac{(n-1)s^{2} }{5.629 }[/tex] ]

                                                  = [ [tex]\frac{14 \times 9409 }{26.12 }[/tex] , [tex]\frac{14 \times 9409 }{5.629 }[/tex] ]

                                                  = [5043.11 , 23401.31]

Therefore, 95% confidence interval for the population variance of the number of tissues per box is [5043.11 , 23401.31].

Answer:

Step-by-step explanation:

You need to subtract the prices of the medium and large from the total

Small = 46.24 - medium -  large

17.50 + 15.75 = 33.75

S = 46.24 - 33.75

S = 12.99

Answer:

42 computers

Step-by-step explanation:

If there is 1 computer per 17 students, then we simply divide the amount of students by 17 to get the amount of computers.

Answer:

42

Step-by-step explanation:

714/17= 42

Answer:

Step-by-step explanation:

0.4

Answer: 0.4

P (Manny wins) + P (Rachelle wins) + P (Peg wins) = 1

0.35 + P (Rachelle wins) + 0.25 = 1

P (Rachelle wins) = 1 - 0.35 - 0.35

P (Rachelle wins) = 0.4

The probability that Rachelle will win any given race is 0.4.

Answer:

Depending on how many people buy hotel rooms, then there is no answer

Step-by-step explanation:

(The question is not specific enough)

Answer:

[tex]2\sqrt[3]{x^{2}y^{2} }[/tex]

Step-by-step explanation:

Answer:

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

Step-by-step explanation:

The equation for the amount of electricity that a solar panel is capable has the following format:

[tex]Q(t) = Q(0)e^{-kt}[/tex]

In which Q(t) is the amount after t years, Q(0) is the initial amount and k is the exponential decay constant.

After ten years, a solar panel produces 89% of the electricity that it was able to produce when it was brand new.

This means that [tex]Q(10) = 0.89Q(0)[/tex]. So

[tex]Q(t) = Q(0)e^{-kt}[/tex]

[tex]0.89Q(0) = Q(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.89[/tex]

[tex]\ln{e^{-10k}} = \ln{0.89}[/tex]

[tex]-10k = \ln{0.89}[/tex]

[tex]10k = -\ln{0.89}[/tex]

[tex]k = \frac{-\ln{0.89}}{10}[/tex]

[tex]k = 0.01165[/tex]

So

[tex]Q(t) = Q(0)e^{-0.01165t}[/tex]

Initially capable of producing 450 watts of power

This means that [tex]Q(0) = 450[/tex]

How long will it take before the solar panel is only able to produce 300 watts of power?

This is t for which Q(t) = 300. So

[tex]Q(t) = 450e^{-0.01165t}[/tex]

[tex]450 = 300e^{-0.01165t}[/tex]

[tex]e^{-0.01165t} = \frac{300}{450}[/tex]

[tex]\ln{e^{-0.01165t}} = \ln{\frac{300}{450}}[/tex]

[tex]-0.01165t = \ln{\frac{300}{450}}[/tex]

[tex]0.01165t = -\ln{\frac{300}{450}}[/tex]

[tex]t = -\frac{\ln{\frac{300}{450}}}{0.01165}[/tex]

[tex]t = 34.79[/tex]

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

The decay constant 'k' for the solar panel's power production can be calculated using the formula for exponential decay, and turns out to be approximately -0.0116. Using this decay constant, it would take approximately 19.5 years for the solar panel to only produce 300 watts of power.

The subject of your question involves an understanding of exponential decay in the context of the power production of a solar panel. The decay is represented by the mathematical formula N=N0exp-kt, where N0 is the initial quantity of the substance, N is the quantity of the substance after time t, k is the decay constant, and e is Euler's number, a mathematical constant approximately equal to 2.71828.

In the scenario you've presented in your question, we know that the solar panel is producing 89% of its original power after 10 years. This can be expressed in our formula as: 0.89 = exp-10k. Solving this equation for k, we'll find that k is approximately equal to -0.0116.

To determine the duration before the solar panel's power production drops to 300 watts, we'll use the same formula, setting N0 at 450 watts and N at 300 watts. Therefore, the equation will be: 300 = 450 * exp-0.0116t. Solving this equation, you'll find that it will take approximately 19.5 years for the solar panel to only produce 300 watts of power.

https://brainly.com/question/2193799

#SPJ12

Answer:

Check step-by-step-explanation.

Step-by-step explanation:

A given criteria for geometric series of the form [tex]\sum_{n=0}^{\infty} r^n[/tex] is that [tex]|r|<1[/tex]. Other wise, the series diverges. When it converges, we know that

[tex] \sum_{n=0}^\infty r^n = \frac{1}{1-r}[/tex].

So,

a)[tex]\sum_{n=0}^\infty (\frac{3}{2})^n[/tex] diverges since [tex]\frac{3}{2}>1[/tex]

b)[tex]\sum_{n=0}^\infty (\frac{1}{2})^n [/tex]converges since [tex]\frac{1}{2}<1[/tex], and

[tex]\sum_{n=0}^\infty (\frac{1}{2})^n= \frac{1}{1-\frac{1}{2}} = \frac{2}{2-1} = 2[/tex]

c)We can use the series in b) but starting at n=1 instead of n=0. Since they differ only on one term, we know it also converges and

[tex]\sum_{n=1}^{\infty}(\frac{1}{2})^n = \sum_{n=0}^{\infty}(\frac{1}{2})^n-(\frac{1}{2})^0 = 2-1 = 1[/tex].

d)Based on point c, we can easily generalize that if we consider the following difference

[tex]\sum_{n=1}^\infty r^n-\sum_{n=0}^\infty r^n = r^0 = 1[/tex]

So, they differ only by 1 if the series converges.

Final answer:

A divergent geometric series has a common ratio (r) greater than 1. A convergent geometric series has a common ratio (r) between -1 and 1. The sums of geometric series that start at n = 0 and n = 1 are different because the first term is included or omitted.

Explanation:

The questions can be answered as -

(a) A geometric series that diverges is an example where the common ratio (r) is greater than 1. An example of a divergent geometric series is: 2 + 4 + 8 + 16 + ...

(b) A geometric series that converges is an example where the common ratio (r) is between -1 and 1. An example of a convergent geometric series starting at n = 0 is: 1 - 1/2 + 1/4 - 1/8 + ... To find its sum, we can use the formula for the sum of a geometric series: S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. Plugging in the values, the sum of this series is 2/3.

(c) A geometric series that starts at n = 1 and converges can have a different sum since the first term is omitted from the calculation. An example of such a series is: 1/2 + 1/4 + 1/8 + 1/16 + ... To find its sum, we use the same formula as in part (b) but with a different first term. In this case, the sum of the series is 1/2.

(d) The sums for a geometric series that starts at n = 0 and n = 1 are different because the first term is included in the sum for n = 0 but omitted in the sum for n = 1.

Answer:

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]

[tex]\mu_{\bar X}= 112[/tex]

[tex]\sigma_{\bar X}=\frac{25}{\sqrt[300}}= 1.443[/tex]

And the best option for this case would be:

b. approximately Normal, mean 112, standard deviation 1.443.

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ of a population, and for this case we know the following info:

Where [tex]\mu=65.5[/tex] and [tex]\sigma=2.6[/tex]

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".

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]

[tex]\mu_{\bar X}= 112[/tex]

[tex]\sigma_{\bar X}=\frac{25}{\sqrt[300}}= 1.443[/tex]

And the best option for this case would be:

b. approximately Normal, mean 112, standard deviation 1.443.

Answer:

$19,747.96

Step-by-step explanation:

You are going to want to use the continuous compound interest formula, which is shown below:

[tex]A = Pe^{rt}[/tex]

A = total

P = principal amount

r = interest rate (decimal)

t = time (years)

First, lets change 5.5% into a decimal:

5.5% -> [tex]\frac{5.5}{100}[/tex] -> 0.055

Next, plug in the values into the equation:

[tex]A=15,000e^{0.055(5)}[/tex]

[tex]A=19,747.96[/tex]

After 5 years, you will have $19,747.96

Answer:

  $500

Step-by-step explanation:

The amount of interest in one year is the product of the interest rate and the account balance:

  I = Prt = $10,000×0.05×1 = $500 . . . . . . interest earned in 1 year

Answer:

x1= 2/3, x2 = -4

Step-by-step explanation:

3x² + 10x + c = 0

Formula for the roots of the quadratic equation is

[tex]x = \frac{-b +/-\sqrt{b^2-4ac} }{2a}[/tex]

Where  a = 3, b=10, c=c  for our equation 3x² + 10x + c = 0.

[tex]x=\frac{-10+/-\sqrt{10^{2}-4*3c} }{2*3} \\\\x=\frac{-10+/-\sqrt{100-12c} }{6} \\\\x_{1} =\frac{-10+\sqrt{100-12c} }{6} \\\\x_{2} =\frac{-10-\sqrt{100-12c} }{6} \\\\x_{1}-x{_2}=\frac{-10+\sqrt{100-12c} }{6} -(\frac{-10-\sqrt{100-12c} }{6} )\\\\x_{1}-x{_2}= \frac{2\sqrt{100-12c} }{6} =\frac{\sqrt{100-12c} }{3} \\\\x_{1}-x{_2}=\frac{\sqrt{100-12c} }{3} = 4\frac{2}{3} =\frac{14}{3} \\\\\sqrt{100-12c} =14\\(\sqrt{100-12c} )^{2}=14^{2}100-12c = 196\\12c=100-196\\c=-8[/tex]

[tex]x=\frac{-10+/-\sqrt{100-12(-8)} }{6} = \frac{-10+/-\sqrt{196} }{6} =\frac{-10+/-14}{6} \\\\x_{1} =\frac{4}{6} =\frac{2}{3} \\x_{2} =\frac{-24}{6} =-4[/tex]

Answer:

$102.96

Step-by-step explanation:

Lets take this one part at a time.

the dealership pays 12000 for the car, so they start at -12000 for how much money they have.

The dealership wants to make a 32% profit.  This means they want to make back the 12000 plus 32% of that.  what is 32% of 12000?  just multiply 12000 bty .32  In the end it works out that the price they sell it for is 15840

I do want to mention that there is a chance the 32% might also be accounting the bonus.  So in other words the dealership spent 12000 for the car then however much in paying the bonus, and they want to make a 32% profit on both of these combined.  I do not think that is what it is asking for, but I wanted to mention it.

Anyway, with a sales price of $15,840 it says the bonus is 6.5% of that.  to find that just do the multiplication .065 * 15840 = 1029.60.  So this is the bonus normally.

Now the question says the salesperson offers a 10 percent discount.  This changes the sales price (by 10%) and the bonus they earn.  let's calculate both.

First 10% discount of the sales price is .9*15840 = 14,256

Then 6.5% of that is .065*14256 = 926.64 So this is the new bonus.

The question wants the difference of the two bonuses, and difference is subtraction.  so 1029.60 - 926.64 = 102.96 So if the salesperson offers a 10% discount they lose $102.96

Answer:

[tex]P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)[/tex]

And we can find this probability using the complement rule and the normal standard distribution and we got:

[tex]P(z>6.302)=1-P(z<6.302)=1-0.99999 \approx 0[/tex]

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the number of attacks of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(510,14.28)[/tex]  

Where [tex]\mu=510[/tex] and [tex]\sigma=14.28[/tex]

We are interested on this probability

[tex]P(X>600)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

[tex]P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)[/tex]

And we can find this probability using the complement rule and the normal standard distribution and we got:

[tex]P(z>6.302)=1-P(z<6.302)=1-0.99999 \approx 0[/tex]

Given the mean and standard deviation for the number of hacking attacks, the z-score for 600 attacks is about 6.30.

The question asks for the likelihood that the group will suffer an average of more than 600 hacking attacks per year over the next 10 years, given that over the past decade the mean number of hacking attacks experienced by members is 510 per year with a standard deviation of 14.28 attacks. Considering the normal distribution of these hacking attacks, we can calculate this probability by finding the z-score corresponding to 600 attacks and then using the standard normal distribution table to find the probability of exceeding this value.

To calculate the z-score for 600 attacks, we use the formula:

Z = (X - μ) / σ

Where X is the value in question (600 attacks), μ (mu) is the mean (510 attacks), and σ (sigma) is the standard deviation (14.28 attacks). Substituting the given values:

Z = (600 - 510) / 14.28 ≈ 6.30

Looking up a z-score of 6.30 in the standard normal distribution table, we find that the area to the left of this z-score is almost 1, meaning the probability of experiencing more than 600 attacks is extremely small, approaching 0. Thus, it is incredibly unlikely that this group will suffer an average of more than 600 attacks in the next 10 years if nothing changes in their environment.