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kompoz [17]
2 years ago
3

Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empiric

al Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.
Mathematics
1 answer:
Arturiano [62]2 years ago
4 0

Answer:

16%

Step-by-step explanation:

Emperical rule states that:

1. About 68% of data fall within 1 standard deviation of mean.

2. About 95% of data falls within 2 standard deviation of mean.

3. About 99.7% of data falls within 3 standard deviation of mean.

Let the time to finish for cyclist be y

P(y>156) = 1 - P(y < = 156)

1 - P(y - u/6 <= 171 -151)

1- P(z<=1)

156 minutes falls within 1 standard deviation, above the mean the Probability of getting more than 156mins is

1- 0.68 /2 = 0.16

0.16 ×100=16%

You might be interested in
A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She sampled 20 frequ
marshall27 [118]

Answer:

c) 44000 miles

Step-by-step explanation:

The regression line has the following format:

y = bx + a

In which b is the slope(how much each mile costs) and a is the fixed number of miles flown.

In this problem, we have that:

a = 24000, b = 10. So

y = 10x + 24000

A person who spent $ 2000 is predicted to have flown:

This is y when x = 2000.

y = 10(2000) + 24000

y = 44000

So the correct answer is:

c) 44000 miles

6 0
2 years ago
Each of three colored cups covers one of three objects. 1) The red cup is somewhere to the left of the white cup. 2) The coin is
yulyashka [42]

Answer:

Shell is under Red color cup

Step-by-step explanation:

We have 3 cups and 3 objects which they cover under them.

Taking into consideration (4) and (2) as they both describe the position related to bean

(4) Gray cup  →Bean (right)     (2) coin ← bean (left)  

that means coin can either under Gray cup or left to gray cup.

Now

(1) Red ← White (left)  (3) Shell → Gray  (right)

This means if we consider coin to be left of gray cup then we can't place shell to the left of gray cup as required in (3)

so coin will be under gray cup

on forming the Color of cups and the coin below them

C1             C2         C3

Red       Gray      White

 __           __          __

Shell        coin        Bean

So Shell is under Red color cup

6 0
2 years ago
Which of these is another way to write the function f(x)=5x?
Alexxx [7]

Answer:

d

Step-by-step explanation:

when f(x)=5......It can also be

f(x)=1/125(625x)

every whole number over one...1(625x)=625x

also 125(1)=125 therefore (625/125)x=5x

6 0
2 years ago
A metal frame is constructed in the form of an isosceles trapezoid. Each base angle measures 80°, the length of the base is 7 fe
jonny [76]
Height of a trapezoid:
h = 5 · sin 80° = 5 · 0.985 = 4.924
x = 5 · cos 80° = 5 · 0.17365 = 0.868
7 - x = 7 - 0.868 = 6.132
By the Pythagorean theorem:
d² = 6.132² + 4.924²
d² = 37.6 + 24.25
d² = 61.85
d = √61.85
d = 7.86 ≈ 8
Answer: The length of a diagonal brace is 8 feet.
3 0
2 years ago
The solutions to the linear differential equation d2u/dt2 = u form a vector space (since combinations of solutions are still sol
maw [93]

Serious high school. This is one of the few differential equations I can solve.

The usual particular solution is u=e^t because e^t is its own derivative.

An independent solution is u=e^{-t} which has a negative sign in the first derivative which turns back to positive in the second.

The arbitrary linear combination spans the solution space:

u= c_1 e^t + c_2 e^{-t}

But we only are asked for the basis.

Answer:\textrm{. } \quad e^t, \quad e^{-t}


5 0
2 years ago
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