Question 2 Allotted time: 15 minutes (plus 5 minutes to submit) A a large national park wants to estimate the mean diameter of all the aspen trees in the park. The park ranger believes that due to environmental changes, the aspon trees are not growing as large as they were in 1975. () Data colleted in 1975 indicate that the distribution of diameter for aspen trees in this park was approximately normal with a mean of a standard deviation of mches. Find the approximate probability that

Answers

Answer 1

Answer:

A park ranger at a large national park wants to estimate the mean diameter of all the aspen trees in the park. The park ranger believes that due to environmental changes, the aspen trees are not growing as large as they were in 1975. (a) Data collected in 1975 indicate that the distribution of diameter for aspen trees in this park was approximately normal with a mean of 8 inches and a standard deviation of 2.5 inches. Find the approximate probability that a randomly selected aspen tree in this park in 1975 would have a diameter less than 5.5 inches.

Step-by-step explanation:

Let X be a random variable which represents the diameters of aspan trees of a park in 1975.

Given that,  X ~ N(8, 2.52)

Mean (μ) = 8 inches

Standard deviation (σ) = 2.5 inches

We have to obtain P(X < 5.5 inches)

We know that if X ~ N(μ, σ²) then, X-M Z=1 ~ N(0,1)

P(X< 5.5) =    P( X- μ < 5.5 - μ)

                           σ         σ

P(X<5.5) = P(Z < 5.5 – 8  )

                               2.5

P(X<5.5) = P(Z < -1)

Using "pnorm" function of R we get, P(Z < -1) = 0.1587

:: P(X < 5.5) = 0.1587

The probability that a randomly selected Aspen  tree in the park in 1975 would have a diameter less than 5.5 inches is 0.1587.


Related Questions

Help ! I don’t know if I have it correct. Can somebody check it out. I got 81/65536 which I know has to be incorrect.

Answers

Answer:  9

Work Shown:

In the numerator, we have 2^2*x^2, which is really just 4x^2. Replace x with 3 and we get 4*x^2 = 4*3^2 = 36.

For the denominator, xy^2, we get

x*y^2 = 3*2^2 = 12

So far we have,

[tex]\frac{2^2x^2}{xy^2} = \frac{4x^2}{xy^2} = \frac{36}{12} = 3\\\\\text{ or simply} \\\\\frac{2^2x^2}{xy^2} = 3[/tex]

when x = 3 and y = 2.

Square both sides to end up with...

[tex]\frac{2^2x^2}{xy^2} = 3\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 3^2\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 9[/tex]

The median and mode of this set of data (23,13,17,11,11)

Answers

Answer:

Mode: 11

Median: 13

Answer:

(23, 13, 17, 11, 11):

Median: 13

Arithmetic mean: 15

Geometric mean: 14.380735416546

Harmonic mean: 13.848764056076

Mode: 11

Standard deviation: 4.5607017003966

Variance: 20.8

Mean Absolute Deviation: 4

Range: 12

Interquartile range: 9

Lower quartile: 11

Upper quartile: 20

Quartile deviation: 4.5

Population size:5

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

Answers

Answer:

A circle with circumference 18 had an arc with 120 central angle.

=> Radius of that circle: R = 18/(2 x pi) = 2.86

=> Length of that arc: L = R x 120 x pi/180 = 2.86 x (2/3) x pi = 5.99

Hope this helps!

:)

Answer:

6

Step-by-step explanation:

Angle: arc length

360 : 18

120 : X

X/120 = 18/360

X = 120 × 18/360

X = 6

In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.

Answers

Answer:

21

Step-by-step explanation:

Answer:

6.7

Step-by-step explanation:

PLEASE ANSWER QUICKLY! Check all that are solutions of the inequality.
-2
0
3.75
4 2/5
1.999
347,595

Answers

Answer:

2,4,5,6

Step-by-step explanation:

Answer:

0, 4 and 2 fifths, 1.999, and 347, 595

or

2, 4, 5, 6

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

I also did the instruction.

Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.



Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places

Answers

Answer:

Hence, Stacy will spin 6,  8.33 times out of her n = 50 attempts.

Step-by-step explanation:

Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.

We will estimate the number of times that she spins a 6 as the expected value of this random variable.

Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.

Then , in this case, with n=50 and p=1/6 we expect to have  number of times of having a 6, which is 8.33.

at the dade county fair, the williams family bought 6 burgers and 4 gatorades for $14.10. the jackson family bought 3 burgers and 4 gatorades for $9.15.find the price of a burger and the price of a gatorade sn: i need help like really fast

Answers

Answer:

The cost of a burger is $1.65 and the cost of a gatorade is $1.05.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

x is the price of a burger.

y is the price of a gatorade.

6 burgers and 4 gatorades for $14.10

This means that [tex]6x + 4y = 14.10[/tex]

3 burgers and 4 gatorades for $9.15.

This means that [tex]3x + 4y = 9.15[/tex]

Will write 4y as a function of x.

[tex]4y = 9.15 - 3x[/tex]

Replacing in the first equation:

[tex]6x + 4y = 14.10[/tex]

[tex]6x + 9.15 - 3x = 14.10[/tex]

[tex]3x = 4.95[/tex]

[tex]x = \frac{4.95}{3}[/tex]

[tex]x = 1.65[/tex]

And

[tex]4y = 9.15 - 3x[/tex]

[tex]4y = 9.15 - 3*1.65[/tex]

[tex]4y = 4.2[/tex]

[tex]y = \frac{4.2}{4}[/tex]

[tex]y = 1.05[/tex]

The cost of a burger is $1.65 and the cost of a gatorade is $1.05.

As a New Year's resolution, Jimmy has agreed to pay off his 4 credit cards and completely eliminate his credit card debt within the next 12 months. Listed below are the balances and annual percentage rates for Jimmy's credit cards. In order to pay his credit card debt off in the next 12 months, what will Jimmy's total minimum credit card payment be?
Credit Card. Current Balance. APR.
A. $563.00. 16%
B. $2,525.00 21%
C. $972.00. 19%
D. $389.00. 17%

a. $321.83
b. $361.45
c. $374.65
d. $411.25

Answers

Answer:

D) FOR BOTH

so 1. D $389.00 17%

2. is D  $411.25

Jimmy's Total Minimum Credit Card Payment must be equal to $71.54 if he is to clear his debt over the next 12 months.

What is Minimum Credit Card Payment (MCC)?

In order for a credit issuer to give an applicant a card, there is a minimum amount that must be deposited into and remain in such a bank account every month. This is what is called a minimum credit card payment.

To calculate Jimmy's MCCP across all cards, we must use the formula:

(APR * Days of Billing Cycle * balance)/365


So for A:

((563 * 30 * 16)/365)/100 = $7.40

For B:

((2,525 * 30 * 21)/365) / 100 = $43.52

For C:

((972 * 30 * 19)/365) / 100 = $15.18

For D:

((389 * 30 * 17)/365) / 100 = $5.44

To get Jimmy's total Minimum Credit Card Payment, we say:

7.40 + 43.52 + 15.18 + 5.44 = $ 71.54

See the link below for more about Minimum Credit Card Payment:

https://brainly.com/question/1245865

A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)

An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?

Answers

Answer:

696.265 inches

Step-by-step explanation:

Radius = 27/2 = 13.5

2 semicircles + 2 lengths

(3.14 × 13.5²) + 2(62)

696.265 inches

Answer:

696

Step-by-step explanation:

If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?

Answers

Answer:

2 divided

Step-by-step explanation:

How many factors does 12 have

Answers

Answer:

6 if you count 1 and 12

Step-by-step explanation:

1*12

6*2

3*4

(1,12,3,4,6,2)

(12,1) (1,12) (3,4) (4,3) (6,2) (2,6)
2 negatives make a positive**
(-12,-1) (-1,-12) (-3,-4) (-4,-3) (-6,-2) (-2,6)

How do you graph -1/4 X. Squared

Answers

Answer:

Points at (0,0) and (4,-1)

Step-by-step explanation:

Mae and Luke are players on a game show. Mae has 80 points and Luke has -20 points. How many more points than Luke does
Mae have?

Answers

Mae has 60 more points
100 more points. -20+100: 80

What is the period of the sinusoidal function?

Answers

Answer:

4

Explanation:

If one period is just how far it takes for one wave to go up and come back down, then we can see one of the waves of the graph starts at 2.5 and ends at 6.5, making the period 4. Of course, there's a more proper formula to it, but this is the easier way my teacher taught me.
Happy studying!

A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is true. Let p ˆ be the proportion in a sample of 100 such ABC batteries. What is the probability that this sample proportion is within 0.05 of the population proportion.

Answers

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

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 proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this question:

[tex]p = 0.8, n = 100[/tex]

So

[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.85 - 0.8}{0.04}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944.

X = 0.75

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

[tex]Z = \frac{0.75 - 0.8}{0.04}[/tex]

[tex]Z = -1.25[/tex]

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

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion


An ice chest contains 4 cans of apple juice, 5 cans of grape juice, 8 cans of orange juice, and 6 cans of mango juice. Suppose that you reach into the container and
randomly select three cans in succession. Find the probability of selecting three cans of apple juice.







Please help I’m stressing and it’s my last question ‼️‼️

Answers

Answer:

(19/23)(18/22)(17/21) or 969/1771

Step-by-step explanation:

You add up the total number of cans, giving you 6+4+5+8 = 23 cans total. From there, you only have 4 cans of grape juice. That means 19 of these cans aren't grape, meaning you are checking the probability of choosing these three times in a row.

The probability of selecting the first can and it not being grape is 19/23. Then, when you select another can in succession, without replacing the cans, you now only have 22 cans left, meaning 18 also will not be grape, so it will be a 18/22 chance. Then, selecting your third can, 21 cans are left, and 17 of them are not grape since you have not yet chosen one, giving you 17/21. You multiply them together.

Hopefully I reduced the fraction properly (or even did this question properly)

which number is located between 1.2 and 1.4 on the number line

Answers

Answer:1.3

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

a number between 2 and 4 is 3

A boat sailed 560 km in 8 hours. It took three hours to travel
the first 150 km. What was its average speed for the
remaining journey?
km/h​

Answers

Step-by-step explanation:

150 km in 3 hours

= 150 ÷ 3 = 50km/h

Remaining distance = 560 - 150 = 410

Remaining hours = 8 - 3 = 5

Then average speed = 410 ÷ 5 = 82 km / h

The average temperature of the atmosphere in the world is approximated as a function of altitude by the relation Tatm=288.15−6.5z where Tatm is the temperature of the atmosphere in K, and z is the altitude in km with z = 0 at sea level. Determine the average temperature of the atmosphere outside an airplane that is cruising at an altitude of 12600 m. The average temperature of the atmosphere outside an airplane is

Answers

Answer:

The average temperature of the atmosphere outside the airplane is [tex]206.25\,K[/tex].

Step-by-step explanation:

The average temperature of the atmosphere outside an airplane flying at an altitude of 12600 meters is computed by evaluating the linear function:

[tex]T (12.6\,km) = 288.15 - 6.5\cdot (12.6\,km)[/tex]

[tex]T (12.6\,km) = 206.25\,K[/tex]

The average temperature of the atmosphere outside the airplane is [tex]206.25\,K[/tex].

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour. Write a function b(t) that would represent this relationship after t hours. Use this function to determine how many bacteria would be in the dish after 10 hours and write it only as a number without units.

Answers

Answer:

[tex]B(t) = 1150*(2)^{t}[/tex]

After 10 hours: 1,177,600

Step-by-step explanation:

The number of bacteria after b hours is given by the following equation:

[tex]B(t) = B(0)(1+r)^{t}[/tex]

In which B(0) is the initial number of bacteria and r is the rate that it increases.

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.

This means that [tex]B(0) = 1150, B(1) = 2*1150[/tex]

So

[tex]B(t) = B(0)(1+r)^{t}[/tex]

[tex]2*1150 = 1150(1+r)^{1}[/tex]

[tex]1 + r = 2[/tex]

[tex]r = 1[/tex]

So

[tex]B(t) = 1150*(2)^{t}[/tex]

After 10 hours:

[tex]B(10) = 1150*(2)^{10} = 1177600[/tex]

1,177,600 bacteria after 10 hours.

What’s the volume of the pic

Answers

Answer:

100[tex]\pi[/tex] cubic cm

Step-by-step explanation:

The volume of a cone can be represented by the formula [tex]\frac{1}{3} \pi r^{2} h[/tex]. Since we know the radius is 5, all we need to find id the height. To do that, we can use the Pythagorean theorem, and see that the height is equal to 12. Plugging the numbers into the formula gives us:

[tex]V =\frac{1}{3} \pi (5^{2}) (12)[/tex]

[tex]V = 100\pi[/tex]

HOPE THIS HELPED! :)

Which equation has the solution x = 12?
(A
4x + 3 = 45
B
5x - 8= 68
2x - 5=29
3x +6=42

Answers

Answer:

D). last one

Step-by-step explanation:

a. 4x+3=45

4x=42

x=10.5 (incorrect)

b. 5x-8=68

5x=76

x=25.2 (incorrect)

c. 2x-5=29

2x=34

x=17 (incorrect)

d. 3x+6=42

3x=36

x=12

Which line is parallel to y = 1/2x -5

Answers

Answer:

Any line with a slope of 1/2 would be parallel to that line.

Step-by-step explanation:

A line is parallel when the slopes are the same, causing the situation where the lines will never intercept. The line in the question has a slope of 1/2, so a parallel line must have that same slope.

What’s the correct answer for this?

Answers

Answer:

A number, such as 10 is a composite number because it is even.

The ten because it’s even

the stained glass below shows bilateral symmetry. The two overlapping squares are congruent. What is the area of the window?

Answers

Answer:

  116.82 square inches

Step-by-step explanation:

The overall shape is that of a 10-inch square with four triangles attached. Each of those is an isosceles right triangle with leg lengths of 2.9 inches.

The area of the four triangles is ...

  total triangle area = 4(1/2)(2.9 in)(2.9 in) = 16.82 in²

The area of the 10-inch square is ...

  square area = (10 in)² = 100 in²

Then the total window area is ...

  window area = 16.82 in² +100 in²

  window area = 116.82 in²

Sally wants to fill ten 8-inch tea glasses. How much tea does she need?
A) 80 ounces
B) 40 ounces
C) 80 cubic inches
D) Not enough information to answer

Answers

Answer

I believe C considering cubic mass

Answer:

D

Step-by-step explanation:

A box below needs to be painted. ​

​How many square inches of paint will be needed to cover the entire surface?



A
80/12 in2
B
61/9 in2
C
49/5 in2
D
77/55 in2

Answers

Answer: c

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Find the arc length of a partial circle with a radius of 5
Will mark brainlist! pleaseeee

Answers

Answer:23.55

Step-by-step explanation:

radius=r=5

Φ=360-90

Φ=270

π=3.14

Length of arc=Φ/360 x 2 x π x r

length of arc=270/360 x 2 x 3.14 x 5

Length of arc=0.75 x 2 x 3.14 x 5

Length of arc=23.55

Answer:

23.55 units

Step-by-step explanation:

Hope this helps!

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY

Answers

Answer:

E 39

Step-by-step explanation:

x+6 = 45

Subtract 6 from each side

x+6-6 = 45-6

x = 39

please ASAP , giving BRAINLIEST if correct.

Answers

Answer:

B. -3(4x + 1) (x - 4)

Step-by-step explanation:

Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).

However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: [tex]-12x^2 + 45x + 12[/tex]

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PLEASE HELP!! ASAP!! I JUST NEED THE ANSWER!!! I WILL MARK YOU BRAINLIEST!!! Which one of the following most accurately demonstrates the flow of energy in an ecosystem? asun's light > predators > producers bproducers > predators > sun's light csun's light > producers > predators dpredators > sun's light > producers