What reason explains why the m

A statistics practitioner determined that the mean and standard deviation of a data set were 120 and 30, is respectively. What c

BartSMP [9]

Answer:

a) 68% of the observations lie between 90 and 150.

b) 95% of the observations lie between 60 and 180.

c) 99.7% of the observations lie between 30 and 210.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Standard deviation = 120

Mean = 30

a. 90 and 150

This is within 1 standard deviation of the mean.

By the Empirical Rule, 68% of the observations lie between 90 and 150.

b. 60 and 180

This is within 2 standard deviations of the mean.

By the Empirical Rule, 95% of the observations lie between 60 and 180.

c. 30 and 210

This is within 3 standard deviations of the mean.

By the Empirical Rule, 99.7% of the observations lie between 30 and 210.

4 0

3 years ago

When running a 100 meter race Bill reaches his maximum speed when he is 45 meters from the starting line and 5 seconds have elap

Mkey [24]

Bill's speed is constant after 5 seconds and 45 meters into the race.

Correct responses:

a. Bill's maximum speed is 8 m/s

b. 24 meters

c. 57 meters

<h3>Methods used to calculate speed and distance traveled</h3>

Given parameters are;

The distance of the race = 100 meter

Distance at which Bill reaches maximum speed = 45 meters

Speed Bill maintains after 5 seconds = The maximum speed

Time at which Bill is 85 meters from the starting line = 10 seconds after start

a. Required;

Bill's maximum speed in meters.

Solution:

Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m

Time at which Bill runs the 40 m at maximum speed, t = 10 s - 5 s = 5 s

$Speed = \mathbf{\dfrac{Distance}{Time}}$

Therefore;

$Bill's \ maximum \ speed = \dfrac{40 \ m}{5 \ s} = \underline{8 \ m/s}$

b. i. Required:

The distance Bill will run for 3 seconds at the maximum speed;

Solution:

Distance, s = Speed, v × Time, t

The distance traveled at maximum speed in 3 seconds is therefore;

Distance = 8 m/s × 3 s = 24 m

The distance Bill travels in 3 seconds at the maximum speed is 24 meters.

ii) The distance Bill travels at 8 seconds after start, is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 3 seconds = 24 meters

Therefore;

Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = 69 meters

c. Bill's distance 6.5 seconds after the start of the race is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters

Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = 57 meters

Learn more about distance, speed, time, relationship here:

https://brainly.in/question/49075584

6 0

2 years ago

Please help! - Kim needs to place 32 mystery books and 56 biography books on library shelves. She is to place the maximum number

Oksi-84 [34.3K]

A. 8 books on each shelf
B. 4 shelves for mystery, 7 shelves for biography

3 0

3 years ago

Read 2 more answers

I’m honestly done with math

rewona [7]

Answer:

15.

Step-by-step explanation:

8x - 10 = 110 (vertical angles are equal in measure).

8x - 10+ 10 = 110 + 10

8x = 120

x = 120 /8

x = 15.

3 0

3 years ago

Jacob decided to ride his bicycle across the country during his 2-month summer vacation. the route he took from washington, dc t

Artist 52 [7]

Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)

Step 2: Use the sentence given to set up an equation

Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"

Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.

Using the sentence we can write the below equation...

$x = 100 + 3(2800 - x)$

Distributing 3 in the right side of the equation, we get...

$x = 100 + 8400 - 3x$

Adding 3x on both sides of the equation, we get...

$x+3x = 8500$

Combine like terms in the left side of the equation, we get...

$4x=8500$

Dividing 4 on both sides of the equation, we get...

$\frac{4x}{4} =\frac{8500}{4}$

Simplifying the fraction on either side of the equation, we get...

$x=2125miles$

Conclusion:

Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be 675 miles.

3 0

3 years ago

What reason explains why the m < Q=115