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jolli1 [7]
3 years ago
6

How do I solve this?: The times of all 15 year olds who run a certain race are approximately normally distributed with a given m

ean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?

Mathematics
2 answers:
ruslelena [56]3 years ago
6 0

Answer:

0.15%

Step-by-step explanation: i took the test

Effectus [21]3 years ago
5 0
We need to 'standardise' the value of X = 14.4 by first calculating the z-score then look up on the z-table for the p-value (which is the probability)

The formula for z-score:
z = (X-μ) ÷ σ

Where
X = 14.4
μ = the average mean = 18
σ = the standard deviation = 1.2

Substitute these value into the formula

z-score = (14.4 - 18) ÷ 1..2 = -3

We are looking to find P(Z < -3)
The table attached conveniently gives us the value of P(Z < -3)  but if you only have the table that read p-value to the left of positive z, then the trick is to do:
1 - P(Z<3)

From the table
P(Z < -3) = 0.0013

The probability of the runners have times less than 14.4 secs is 0.0013 = 0.13%


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Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times t
lidiya [134]
Well first you have to make variables for each number.
1st - x
2nd - y
3rd - z

first sentence says twice first number so 2x. is means equals so =. eleven more than sum of the other two numbers. sum of other two numbers is (y + z) and eleven more than that is (y + z) + 11. So so this sentence says:
2x = (y + z) + 11

second sentence says sum of twice the first and three times third. twice first is 2x and three times third is 3z. their sum would be (2x + 3z). It it says is one more than second number. So = (y + 1). So so this means:
(2x + 3z) = (y + 1)

third sentence says second number (y) is is equal to sum of first and third (x + z). so;
y = (x + z)

now for the work.

We we can easily solve for a by subtracting the first 2 equations. the way to subtract 2 equations is by subtracting one left side of equal sign from the other equations left side and then doing the same with the right side.

So we will subtract the 1st and second equations we made.
So so left sides would be
2x - (2x + 3z)
2x - 2x - 3z
-3z

right side would be:
y + z + 11 - (y + 1)
y + z + 11 - y - 1
z + 10

now put the sides with an equal sign
-3z = z + 10
-4z = 10
z = -2.5

now we can plug in z into the equations and subtract second and third equations. But but we will subtract opposite sides. So so left minus right and right mi is left after we plug in z:
(2x + 3 (-2.5)) - (x + (-2.5))
2x - 7.5 - x + 2.5
x - 5

other one would be
(y + 1) - y
1

So so put an equal sign and get:
x - 5 = 1
x = 6

now plug x and x into 3rd equation
y = x + z
y = 6 + (-2.5)
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now we have values. You can check answer by plugging values into other 2 equations
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Step-by-step explanation:

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x^2+5x+6x+30

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