A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours.
(a) Identify the parameters in this situation.
(b) Identify the statistics in this situation.
(c) Suppose we were to make a histogram of the finishing times of all participants in the duathlon. Which of the following would the histogram be a display of?
i. Population distribution
iii. Distribution of a sample
ii. Sampling distribution of means
(d) Suppose the process of taking random samples of size 30 is repeated 200 times and a histogram of 200 sample means is created. Which of the following would the histogram be a display of?
i. Population distribution
ii. Distribution of a sample
iii. Sampling distribution of means
(e) What is the standard error for the mean finish time of 30 randomly selected participants?
(f) If one participant is selected at random, what is the probability that his/her time will be less than 1.59 hours.
(g) What is the probability that another sample of 30 randomly selected participants will have a mean finishing time of 1.59 hours or less?

Answers

Answer 1

Answer:

A.) Parameter = 1.67 ; 0.25

B.) Statistic = 1.59, 0.30

C.) Population distribution

D.) Sampling distribution of means

E.) 0.058

F.) 0.395

G.) 0.072

Step-by-step explanation:

A.) The parameters are measured quantities or characteristics derived from the population. The parameter here describes the mean and standard deviation of all participants ;

Population mean = 1.67

Population standard deviation = 0.25

B.) Statistic are measured quantities which are characteristics of the sample. Here, we have the sample mean and standard deviation

Sample mean = 1.59

Sample standard deviation = 0.30

C.) The population distribution is the plot of the histogram prepared using data from the population (all participants)

D.) The plot of the mean value obtained from the repeated measurement or simulation of the sample data is called sampling distribution of the means.

E.) Mean finish time of 30 randomly participants :

Sample size, n = 30

Standard Error = s/√n

Standard Error = 0.30 /√30 = 0.0548

F.) If one participant is selected at random, what is the probability that his/her time will be less than 1.59 hours

P(x < 1.59)

Z = (xbar - μ) / σ ; (1.59 - 1.67) / 0.30 = - 0.267

P(Z < - 0.267) = 0.395 (Z probability calculator)

G.) P(x < 1.59)

Z = (xbar - μ) / s ; (1.59 - 1.67) / (0.30/√30) = - 1.46

P(Z < -1.46) = 0.072 (Z probability calculator)


Related Questions

Equations of Exponential Functions

Find the missing values for the exponential function represented by the table below.

a. 7.5
5
b. -16.875
25.3125
c. 16.875
25.3125
d. -16.875
-25.3125

Please select the best answer from choices provided

Answers

Answer:

C. 16.875

   25.3125

Step-by-step explanation:

I calculated it logically

NEED HELP FAST WILL GOVE THE BRAINLEST

Answers

Answer:

us my understanding the answer is B

Step-by-step explanation:

y=8x-3

8x-y=3

3/8

y=8x+9/5

0=8x9/5

x=9/40

Tamara uses 8.5 of blue paint and white paint to paint her bedroom walls. Three fourths of this amount is blue paint, and the rest is white paint . How many pints of white paint did she used to paint her bedroom walls

Answers

The amount of white paint used by Tamara to paint the bedroom walls is 2.125.

What are Fractions?

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Total amount of paint = 8.5

Three fourths of this amount is blue paint.

Amount of blue paint = (3/4) × 8.5 = 6.375

Rest is white paint.

Amount of white paint = Total paint - Amount of blue paint

                                     = 8.5 - 6.375

                                     = 2.125

Hence the amount of white paint used to paint bedroom walls is 2.125.

To learn more about Fractions, click on the link :

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A line goes through (-4,-5) and (2,-3). Write an equation that is perpendicular to the line above

Answers

9514 1404 393

Answer:

  y = -3x

Step-by-step explanation:

The slope formula gives the slope of the segment between the given points.

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -(-5))/(2 -(-4)) = 2/6 = 1/3

The slope of the perpendicular line is the opposite reciprocal of this, so is ...

  m' = -1/(1/3) = -3

A perpendicular line is ...

  y = -3x

Pls help I’ll brainlest and add extra points

Answers

Answer:

26. D) $252

27. A) -6.7 + 6.8

Step-by-step explanation:

26. 400 * 0.3 = 120

400 - 120 = 280

280 * 0.1 = 28 (because the 10% is additional, cannot add it to the original 30%)

280 - 28 = 252

27. -4.5 + 4.4 = -0.1

- 6.7 + 6.8 = 0.1

-0.1 + 0.1 = 0

which is best represented by the following equation 55x + 75.25 = 680.25

Answers

Answer:

11

Step-by-step explanation:

680.25-75.25=605

605÷55=11

Answer:

11

Step-by-step explanation:

Amanda is training for a marathon. She runs 7 1/2 miles every 3 days. At this rate, how many miles will she run in 36 days?​

Answers

Answer:

She would run 90 miles in 36 days

You would start off by doing 7.5 ÷ 3 to get 2.5

Then you multiply 2.5 by 36 to get 90

PLEASE HELP, EXPLAIN HOW YOU GOT YOUR ANSWER AFTER PLEASE .

Answers

Answer:

Area = 288 m²

Step-by-step explanation:

The area of the shape given = area of the square + area of the triangle

= (side length)² + ½*base*height

side length = 16 m

base = 16 - 8 = 8 m

height = 8 m

Plug in the values into the equation

Area = 16² + ½(8)(8)

Area = 256 + 32

Area = 288 m²

Which type of transformation is represented by the following two angles?
*******Only answer if u know it please*****

Answers

Answer:

Dilation

Step-by-step explanation:

Dilation becuase the side lengths expand and produce non rigid motion and dilation is the only non rigid transformation.

Answer:

its a dilation

Step-by-step explanation:

A dilation is a transformation that produces the same shape as the original but of a different size

There are 7 brown cars out of 35 cars. What is the ratio of brown cars to the cars?

Answers

7:35 would be the ratio hope this helps! :))

Answer:

7:35 (can also be written as 7/35)

Step-by-step explanation:

is 3/8 bigger than 45/100

Answers

no, 45/100 is greater. 3/8 as a decimal is .
0.375 and 45/100 is 0.45 the tenth place is larger making the number larger

To prevent deer from running across highways, researchers are investigating sound-emitting devices that would frighten deer before they reach the highway. As part of the investigation, the researchers set up 20 devices along a two-mile stretch of road. When a deer approached a device, the device would activate and emit a sound. The researchers recorded whether the deer moved toward the highway (positive response), away from the highway (negative response), or did not move (neutral response).

The researchers kept the loudness of the sound constant at 60 decibels. However, they varied the pitch of the sound. There were 6 treatment levels, all measured in kilohertz (kHz): 0, 0.28, 1, 8, 15, and 28. The order of the treatments was randomly assigned.

(a) The control in the experiment was 0 kHz, or no sound. What information is gained by using the control with no sound that could not be obtained if no control were used?
(b)(i) What is one advantage to keeping the loudness at a constant 60 decibels for all treatments?

(b)(ii) What is one disadvantage to keeping the loudness at a constant 60 decibels for all treatments?

(c) The results of the experiment are shown in the following bar chart.
Based on the results, would you recommend using a sound-emitting device to keep deer from running across highways? Explain your answer.

Answers

Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.

(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.

(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness

(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.

Step-by-step explanation:

Final answer:

The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.

Explanation:

Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.

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Which graphs show continuous data?


Select each correct answer.

HELP ME PLEASE!!!

Answers

Answer: the bottom two graphs show continuous data

Step-by-step explanation:

6. Which fraction is equal to 30%

Answers

3/10 is equal to 30%.

Answer:

3/10

Step-by-step explanation:

Number that appears the most in a given set of data
A) Mean
B.) Median
C) Mode
D) Range

I'll give brainliestttt​

Answers

The answer is: Mode.
It appears most in a given set of data.

Tom's toy box is shown below. The toy box is shaped like a rectangular prism: It has 5 wooden faces and is open on the top.

What is the total surface area of the 5 fades of the toy box that are wooden?

O A 1,100 squares inches

O B 3,009 square inches

O C 900 square inches

O D 255 square inches

Don’t answer if you don’t know, and whoever answers correctly will get Brainliest. :)

Answers

Answer:

O C 900 square inches

for 20 please help TT

Answers

Answer:

a

Step-by-step explanation:

Find the circumference of a circle with a diameter of 50 centimeters

Answers

Answer:

157.08 is the circumference. Hope it helps you

Step-by-step explanation:

A sailfish can swim u to 68 miles per hour. At this rate, how far can a sailfish swim in 1/4 hour?
A. 34 mi.
B. 27.2 mi.
C. 17 mi.
D. 10.2 mi.

Answers

Answer:

C. 17 miles

Step-by-step explanation:

Divide 68 by 4 since it is a fourth of an hour

Which is not a factor pair of 300

Answers

Answer:

Step-by-step explanation:

So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. [Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300.

QUESTION 9 of 10: Mutual funds can be:
a) Purchased in any amount
b) Can be focused on a single asset class
c) Invested by sector
d) All the above
Submit

Answers

Maybe A because that’s seem the best

Answer: d) All of the above

Step-by-step explanation:

Please Help Help Help

Answers

EDCB is a rectangle, so:

ED = BC = 12

DC = EB = 29

We know that,

= AB = AE + EB

= 34 = AE + 29

= 34 - 29 = AE

= 5 = AE

Now, in triangle EAD, by pythagonas theoram:

= H² = P² + B²

= H² = 5² + 12²

= H² = 25 + 144

= H = √169

= H = 13

So, AD = 13 cm

_________________

Simpooooool

How many pints are needed for 2 3/4 pots of soup?

Answers

Answer:

1.38

Step-by-step explanation:

2 cups is one pint so if 3/4 is .38 then you would put it together to get 1.38

Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214?

Answers

Answer:

To show 1214 using place value blocks, you would need at least 4 blocks: one thousand block, two hundred blocks, one ten block, and four ones blocks. If you have fewer than 4 blocks, it is not possible to show 1214 using place value blocks.

If you have exactly 4 blocks, you can show 1214 in only 1 way: using 1 thousand block, 2 hundred blocks, 1 ten block, and 4 ones blocks.

If you have exactly 5 blocks, you can show 1214 in 2 ways: using 1 thousand block, 2 hundred blocks, 1 ten block, and 4 ones blocks, or using 2 thousand blocks, 1 hundred block, 2 ten blocks, and 4 ones blocks.

If you have exactly 6 blocks, you can show 1214 in 3 ways: using 1 thousand block, 2 hundred blocks, 1 ten block, and 4 ones blocks, using 2 thousand blocks, 1 hundred block, 2 ten blocks, and 4 ones blocks, or using 1 thousand block, 1 hundred block, 3 ten blocks, and 4 ones blocks.

Therefore, if you have fewer than 10 place value blocks, you can show 1214 in 3 different ways.

y=x+8 y=9x+72 substitution

Answers

(Y,X) = (72,8)
I think this is the right answer it has been a while since I had math sorry. Hope this helps

Pyramid A is a right square pyramid with a height of 133m and a square base with a perimeter of 492m. Pyramid B has a square base with a perimeter of 592m and a height of 247m. Which pyramid has the greater volume and by how many times as​ great?

Answers

9514 1404 393

Answer:

  Pyramid B is 2.6888 times the volume of pyramid A

Step-by-step explanation:

The volume is proportional to the height, and to the square of the linear measure of the base.

Then the ratio of volumes will be ...

  B/A = (592²·247)/(492²·133) = 86564608/32194512 ≈ 2.6888

Pyramid B has the greater volume by a factor of about 2.6888.

_____

Additional comment

The actual volumes in cubic meters will be 1/48 of the numbers we used in the ratio above.

If you recall that the side length is related to the perimeter by ...

  P = 4s   ⇒   s = P/4

and the volume is ...

  V = 1/3s²h

Then you have ...

  V = 1/3(P/4)²h = 1/48·P²h . . . . . . P²h is the number we used above

Please help ill give u brainlest 30 points !!

Paige had a lemonade stand. She sold s small cups of lemonade for $1 each, m medium cups for $3 each, and l large cups for $5 each. At the end of the day, she had sold 6 medium cups, 9 large cups, and 12 small cups of lemonade.

Which expressions show how much money Paige made selling lemonade? Select all that apply.

A. 12s + 9m + 6l

B. 1s + 3m + 5l

C. $75

D. $93

Answers

Answer:

B

Hope this helps!

approximate v46 to the nearest hundredth ​

Answers

Answer:

6.78

Step-by-step explanation:

100 PTS
Use the table to determine the appropriate model of the function,

x 0 1 2 3 4
f(x) 3 7 29 87 199
a. linear
b. quadratic
c. cubic
d. exponential

Answers

Answer:

The answer is D. An Exponential Function.

Step-by-step explanation:

So the table is setup as;

x :   0     1      2     3      4

f(x): 3    7     29    87    199

If you plot the points on the coordinate plane, the value of x increases, and value of y increases .

It is not linear, because slope between two points is not the same, so you can rule that one out.

It´s not quadratic or cubic, because it is not intercepting the x axis.

So, it can only be D, an exponential function since we ruled out every other option.

I hope this helps :))

22 is 22% of?

How do I find the answer?

Answers

Answer:

4.84

Step-by-step explanation:

Do 100 divided by 22% that's gonna give you 0.002 so then you drop the two zeros after the decimal and you gonna have 0.22 then do 0.22 times 22 and you gonna get your answer 4.84.

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