Who is sigma Lazyeight?

1 point) As reported in "Runner's World" magazine, the times of the finishers in the New York City 10 km run are normally distri

BigorU [14]

Answer:

(a) E (X) = 61 and SD (X) = 9

(b) E (Z) = 0 and SD (Z) = 1

Step-by-step explanation:

The time of the finishers in the New York City 10 km run are normally distributed with a mean,μ = 61 minutes and a standard deviation, σ = 9 minutes.

(a)

The random variable X is defined as the finishing time for the finishers.

Then the expected value of X is:

E (X) = 61 minutes

The variance of the random variable X is:

V (X) = (9 minutes)²

Then the standard deviation of the random variable X is:

SD (X) = 9 minutes

(b)

The random variable Z is the standardized form of the random variable X.

It is defined as: $Z=\frac{X-\mu}{\sigma}$

Compute the expected value of Z as follows:

$E(Z)=E[\frac{X-\mu}{\sigma}]\\=\frac{E(X)-\mu}{\sigma}\\=\frac{61-61}{9}\\=0$

The mean of Z is 0.

Compute the variance of Z as follows:

$V(Z)=V[\frac{X-\mu}{\sigma}]\\=\frac{V(X)+V(\mu)}{\sigma^{2}}\\=\frac{V(X)}{\sigma^{2}}\\=\frac{9^{2}}{9^{2}}\\=1$

The variance of Z is 1.

So the standard deviation is 1.

8 0

1 year ago

30 POINTS! Monica paid sales tax of $1.50 when she bought a new bike helmet. if the sales tax rate was 5%, how much did the stor

avanturin [10]

Hmm... well, here ya go.

1.50 ÷ 0.05 = 30
So, the total is $30
As for the tax rate, including the total, it would be $31.50.

Hope I helped.

6 0

1 year ago

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max is bisecting a segment. first. he places the compass on one endpoint and opens it to a width larger than half of the segment

spin [16.1K]

Answer:

Keep the compass the same width and place it on the other endpoint.

Step-by-step explanation:

Max is bisecting a segment. First, he places the compass on one endpoint and opens it to a width larger than half of the segment. Then he swings an arc on either side of the segment.

Next Max's step should be: keep the compass the same width and place it on the other endpoint.

He will draw the second arc of the same radius as the first one.

Two drawn arcs intersect at two points, Max will connect these points and get the segment which bisects the given one.

7 0

2 years ago

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Drag each object to show whether distance is proportional to time in the situation represented. A horse running around a race tr

lesya692 [45]

Answer:

Situation Relation

1 Distance is not proportional to time.

2 Distance is proportional to time.

3 Distance is proportional to time.

4 Not much information.

Step-by-step explanation:

We are required to match the options to whether distance is proportional to time in the following situations.

1. A horse running around a race track.

Since, the horse is running around the race track. So, the speed of the horse can vary at different time

So, distance is not proportional to time.

2. A truck passing through 4 cities at a constant speed.

As, Distance = Speed × Time and we are given that the speed is constant.

So, distance is directly proportional to the time.

3. A dog jogging at a constant speed for 20 minutes.

As, Distance = Speed × Time and we are given that the speed is constant.

So, distance is directly proportional to the time.

4. A person running down a field to score a touchdown.

Since, there is no information about the speed of the person.

But, as the person is running to score a touchdown, he may run at a constant speed.

So, there is not much information.

Hence, we have,

Situation Relation

1 Distance is not proportional to time.

2 Distance is proportional to time.

3 Distance is proportional to time.

4 Not much information.

6 0

1 year ago

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Which statements about the graph of the function f(x) = 2x^2– x – 6 are true? Select two options.

Alekssandra [29.7K]

Answer:

Step-by-step explanation:

Please, share the answer options next time.

1) f(x) = 2x^2– x – 6 is a quadratic function.

2) The coefficients of this polynomial are a = 2, b = -1 and c = -6

2) Its graph opens up.

3) The x-value of the axis of symmetry and the vertex is x = -b / (2a), which here comes out to x = -(-1) / [2(2)], or x = 1/4

4) the y coordinate of the vertex is f(1/4), or -6 1/8

5) The vertex is at (1/4, -6 1/8)

6) The y-intercept is at f(0): 2(0)^2 - 0 - 6 = -6 => (0, -6)

3 0

1 year ago

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