Yuki and Zana are on a swimming team. They often compete against each other in the 100 meter freestyle race. Yuki's times in this race are normally distributed with a mean of 808080 seconds and a standard deviation of 4.24.24, point, 2 seconds. Zana's times are also normally distributed with a mean of 858585 seconds and a standard deviation of 5.65.65, point, 6 seconds. We can assume that their times are independent.
Suppose we choose a random 100 meter freestyle race and calculate the difference between their times.
Find the probability that Yuki's time is faster than Zana's.
You may round your answer to two decimal places.

Answers

Answer 1

Answer:

0.2389 = 23.89% probability that Yuki's time is faster than Zana's.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Subtraction of normal variables:

When normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Yuki's times in this race are normally distributed with a mean 80 seconds and standard deviation of 4.2 seconds. Zana's times are also normally distributed with a mean of 85 seconds and a standard deviation of 5.6 seconds.

Yuki's is faster than Zana if the subtraction of Yuki by Zana is larger than 0.

The mean is:

[tex]\mu = 80 - 85 = -5[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{4.2^2 + 5.6^2} = 7[/tex]

Find the probability that Yuki's time is faster than Zana's.

This is P(X > 0), which is 1 subtracted by the pvalue of Z when X = 0.

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

[tex]Z = \frac{0 - (-5)}{7}[/tex]

[tex]Z = 0.71[/tex]

[tex]Z = 0.71[/tex] has a pvalue of 0.7611

1 - 0.7611 = 0.2389

0.2389 = 23.89% probability that Yuki's time is faster than Zana's.


Related Questions

There are 4 roses for every 7 carnations in a bouqeuet. Mr rodriguez buys a bouqeuet with 12 roses in it. How many total flowers are in the bouqeuet Mr rodriguez bought?

Please explain step by step I dont get it.

Answers

Answer:

33 total flowers are in the bouquet Mr Rodriguez bough

Step-by-step explanation:

So for every 4 roses there are 7 carnations meaning the ratio is 4:7

4 times x = 12

x=3

So we do the same for carnations

7 x 3 = 21

Now we add to find the total

21+12=33

33 total flowers

brainiest exchange give me and I will give you 2+2​

Answers

Answer:

4

Step-by-step explanation:

and sure

Answer:

4

Step-by-step explanation:

please help meeeee i will give brainlyest

Answers

Answer:

answer is 63 min

Step-by-step explanation:

math+calculator   like and subscribe to yourmom.com31  

8% of $796.25 is how much?

Answers

8/100*796.25

=63.7%

Answer:63.7%

Answer: Hello, there! your Answer is below

63.7 would Be the correct answer

Step-by-step explanation: Below Is Info About How to Calculate Precentage UwU

how to calculate percentage of a number. Use the percentage formula: P% * X = Y

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

how to solve by factoring
x^2 + x = 0

Answers

Answer:

x=0 and x=-1

Step-by-step explanation:

Given: x^2+x=0

Factor: x(x+1)=0

Use Zero Product Property: x=0 and x+1=0

Therefore, x=0 and x=-1

what is the area of the shaded region? use 3.14 for pi

Answers

Answer:

13.8

Step-by-step explanation:

Area of square = πr²

=22/7 × 4²

=50.2

Area of square = l²

=8²

= 64

Area of shape is 64 - 50.2 = 13.8

Answer:

The answer is 13.8

Step-by-step explanation:

Yes

PLEASE GIVE ME AN ANSWER!!!!ILL MARK BRAINLIEST ANSWER

Answers

Answer:

3 3/4

Step-by-step explanation:

3.75 square ft per hr.

5/8 x 6 = 3.75

3 3/4.

I got this question

If Mike loses $5 per week, how much does he lose in 4 weeks?

Answers

Answer:

$ 20

Step-by-step explanation:

[tex]1week \: = 5 \\ 4 \: weeks = x \\ \\ x = 20[/tex]

hope this helps you.

Can I have the brainliest please?

Have a nice day!

Pam and her grandma are planning to make a quilt together. The quilt will be made out of fabric squares that measure 6 inches on each side. The quilt will have 3 more squares along its longer edge than it will have along its shorter edge.
If there are x fabric squares along the quilt's shorter edge, find an expression for f(x), the length of the quilt's shorter edge in inches.
f(x)=
6x
Next, find an expression for g(x), the length of the quilt's longer edge in inches.
g(x)=
Which function can you use to find the area of the quilt in square inches?

Answers

Answer:

There are x squares on the shorter side, each square measures 6 inches.

The length of the shorter side is:

f(x) = x*6 = 6x

The length of the longer side is:

g(x) = (x + 3)*6 = 6x + 18

The area of the quilt is:

A = 6x(6x + 18) = 36x² + 108x

If x=3 and y=7, evaluate the following expression: 100 − 3 ( 3 − 4x )

Answers

Answer:

[tex]100 - 3(3 - 4x) \\ = 100 - 3(3 - 4 \times 3) \\ = 100 -27 \\ = 73[/tex]

Answer:

873

Step-by-step explanation:

100 - 3 ( 3- 4x ) 97 ( 3 - 4×3 )97 (3 - 12 ) 97 × 9 873

The side lengths of a rectangle are all multiplied by 5. What happens to its perimeter?

Answers

Answer:

The perimeter is multiplied by 5.

Step-by-step explanation:

Perimeter of a rectangle:

The perimeter of a rectangle with sides l and w is given by:

[tex]P = 2(l + w)[/tex]

The side lengths of a rectangle are all multiplied by 5.

This means that [tex]l = 5l, w = 5w[/tex]. So

[tex]P_M = 2(5l + 5w) = 2*5(l+w) = 10(l + w)[/tex]

What happens to its perimeter?

The rate is:

[tex]\frac{P_M}{P} = \frac{10(l+w)}{2(l+w)} = 5[/tex]

The perimeter is multiplied by 5.

find the gradient of the line
with the equation 3x+4y=10

Answers

The gradient of the line with that equation is -3/4

50 pts please help asap (:

Answers

Answer:

d. 8 units

Step-by-step explanation:

If AC = 16 units then the length of CB is 8 units because DB is perpendicular bisector from the centre of circle.

Answer: B

Step-by-step explanation: I took the quiz

Hope this helps

A LOT OF POINTS!!
Suppose you borrow $40,000 at 13% APR for a 12-year term to be paid monthly. Your monthly payment is $450.00.

How much of your first payment goes toward interest?

Make sure you show your work to earn full credit.

Answers

Answer:

You get $45,200 first with interest with the 5400 you made in 1 year that dedeucts

Step-by-step explanation:

-A sequence is a list of numbers or obje
What is a pattern?
-A pattern is a repetitive sequence and
numbers and almost everywhere you ca
What's More
A. Directions: Give the pattern rule of t
Rul
1. 1, 4, 7, 10, 13
2.2, 8, 32, 128, 512
Rul​

Answers

Answer:

1. Add 3

2. Multiply 4

Step-by-step explanation:

Given

[tex](1)\ 1, 4, 7, 10, 13[/tex]

[tex](2)\ 2, 8, 32, 128, 512[/tex]

Required

The rule

[tex](1)\ 1, 4, 7, 10, 13[/tex]

This is a linear function because successive terms have a common difference

The common difference between each term is:

[tex]d = 4 - 1 = 3[/tex]

[tex]d = 7 - 4 = 3[/tex]

[tex]d = 10 - 7 = 3[/tex]

[tex]d = 13 - 10 = 3[/tex]

The above shows that 3 is [tex]added\ to\ each\ term[/tex] to get the next term.

Hence, the rule is: Add 3

[tex](2)\ 2, 8, 32, 128, 512[/tex]

This is a geometric function because successive terms have a common ratio

The common ratio between each term is:

[tex]r = 8/2 = 4[/tex]

[tex]r = 32/8 = 4[/tex]

[tex]r = 128/32 = 4[/tex]

[tex]r = 512/128 = 4[/tex]

The above shows that 4 [tex]is\ multiplied\ to\ each\ term[/tex] to get the next term.

Hence, the rule is: Multiply 4

what is the area of a right triangle with sides 7ft 24ft and 25ft?

Answers

The area of the right triangle is 84

Answer:

84 ft^2

Step-by-step explanation:

[tex] \frac{7 + 24 + 25}{2} = 28[/tex]

The area is:

[tex] \sqrt{28 \times (28 - 7) \times (28 - 24) \times (28 - 25)} [/tex]

[tex] = 84 \: {ft}^{2} [/tex]

I need so much help help me please UwU

Answers

Answer:

Line A: y = 3x + 3

Line B: y = -1/3x + 3

Step-by-step explanation:

Line A points: (0, 3) and (1, 6)

Slope:

m=(y2-y1)/(x2-x1)

m=(6-3)/(1-0)

m= 3

y - y1 = m(x - x1)

y - 3 = 3(x - 0)

y - 3 = 3x

y = 3x + 3

Line B points: (0, 3) and (9, 0)

Slope:

m=(y2-y1)/(x2-x1)

m=(0-3)/(9-0)

m= -1/3

y - y1 = m(x - x1)

y - 3 = -1/3(x - 0)

y - 3 = -1/3x

y = -1/3x + 3

In sixteen years Paul will be 48 years old.
How old is he now?

Answers

Answer:

32 years old

Step-by-step explanation:

48-16=32

Answer:

Paul is 32 years old

Step-by-step explanation:

48 - 16 = 32

Do 5 yd 12 yd 13 yd make a right angle?

Answers

Nope it does not nope it does not make one

Kristin charges $30 to train a small dog, and $50 to train a big dog. If Kristin trains 15 small dogs and 6 big dogs, how much money will she make?

Answers

Answer:

$750

Step-by-step explanation:

We can set up the equation 30x + 50y =  z where x = the amount of small dogs, y = the amount of big dogs, and z = the total.

After plugging in the x and y values to solve for z, we are left with the following equation:

30(15) + 50(6) = 750

Tinisha is planning a birthday party. She can buy:
10 balloons, 8 cupcakes, and 8 hats for $50
5 balloons, 9 cupcakes, and 7 hats for $46, or
12 balloons, 7 cupcakes, and 9 hats for $51
Using b for the number of balloons, c for the number of cupcakes, and h for
the number of hats, write a system of equations to represent this situation.

Answers

Answer:

b+c+h=50

Step-by-step explanation:

Its the first one because you need to have the same amount of hats as cupcakes cause the hat really stands for people.

Calculate the mass of NaOH in 0.2 moles of NaOH

Answers

Answer:

0.2M i.e

Step-by-step explanation:

SAT scores: The College Board reports that in 2009, the mean score on the math SAT was 582 and the population standard deviation was =σ120. A random sample of 20 students who took the test in 2010 had a mean score of 515. Following is a dotplot of the 20 scores. (a) Are the assumptions for a hypothesis test satisfied? Explain. (b) If appropriate, perform a hypothesis test to investigate whether the mean score in 2010 differs from the mean score in 2009. Assume the population standard deviation is =σ120. What can you conclude? Use the =α0.10 level of significance and the critical value method.

Answers

Answer:

we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.

Step-by-step explanation:

H0 : μ = 582

H1 : μ < 582

Test statistic :

T = (xbar - μ) ÷ σ/√n

Xbar = 515 ; n = 20 ; σ = 120

T = (515 - 582) ÷ 120/√20

T = -67 / 26.832815

T = 2.50

Pvalue at t score = 2.50 ; df = 19 is 0.0187

At α = 0.0187

Pvalue > α ; Hence, we fail to reject the Null

Hence, we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.

sin(30°)cos(45°) + cos(30°)sin(45°)

Answers

Step-by-step explanation:

sin(30°)cos(45°) + cos(30°)sin(45°)=1+√3/2√2

sin30 = 1/2
cos45 = √2/2
cos30 = √3/2
sin45 = √2/2
answer: √2 + √6
—————
4

7n - 4 (8n+4) = 159

Answers

Answer:

n = -7

Step-by-step explanation:

Use distributive property:

7n - 32n - 16 = 159

Combine like terms

-25n - 16 = 159

Add 16 to both sides to isolate variable n

-25n = 175

Divide both sides by -25 to isolate variable n

n = -7

Check your work:

7(-7) - 32(-7) - 16 = 159

-49 + 224 - 16 = 159

159 = 159

Which number has the least absolute value?

Answers

A.

Explanation: The bigger the negative number, the lower the number actually is.

What is the theoretical probability that the spinner below will land on 6 if someone spins it 48 times?

Answers

Answer:

1/4 or 12*

Step-by-step explanation:

There are 8 possibilities.  2 of them are 6.

2/8=1/4

1/4 of 48 is 12

*The theoretical probability doesn’t change no matter how many times you spin the spinner.  It will always be 1/4.  (Or 0.25, or 25%). That could be what they’re asking.  If you spun it 48 times, it would probably land on a six 12 times.  That could also be what they’re asking for.  12:48 = 1:4.

A bicycle is originally priced at $60. The online retailer gives a discount and the bicycle is now priced at $42. Enter the percentage discount for the cost of the bicycle.

Answers

Answer:

30% ywww

Step-by-step explanation:

Can someone give me a fake band name???

Answers

Answer:

loaded diper

Step-by-step explanation:

what is the shape identify in the image

Answers

Answer:

it is a triangular prism

It is a Triangular prism
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