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sertanlavr [38]
3 years ago
5

John drives to work each morning and the trip takes an average of µ = 38 minutes. The distribution of driving times is approxima

tely normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take less than 35 minutes?​
Mathematics
1 answer:
exis [7]3 years ago
5 0

Answer:

The probability that John’s drive to work will take less than 35 minutes is 0.2743

Step-by-step explanation:

Given : \mu = 38 \\\sigma = 5

To Find :what is the probability that John’s drive to work will take less than 35 minutes?​

Solution:

\mu = 38 \\\sigma = 5

We are supposed to find P(x<35)

We will use z score

Formula: z=\frac{x-\mu}{\sigma}

Substitute x = 35

z=\frac{35-38}{5}

z= −0.6

Refer the z table for p value

P(x<35)= 0.2743

Hence the probability that John’s drive to work will take less than 35 minutes is 0.2743

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Answers:

length of rope = 2 meters

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=========================================================

Explanation:

Assuming there are no structures (buildings, fences, etc) to get in the way of the goat, this means the goat's area that it can roam is a circle with radius r

The area of the circle is pi*r^2 which is equal to 12.56 square meters

pi*r^2 = 12.56

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r^2 = 4

r = sqrt(4)

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The radius of the circle is 2 meters. This is the length of the rope. If the goat goes out as far as it can go, and tries to move left/right, then it will trace out a circle of radius 2. This is assuming the rope is kept fully taut the entire time.

The perimeter of the circle is the same as the circumference

circumference = 2*pi*r

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circumference = 4*pi

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The circumference and area are the same because r^2 = 4 and 2*r = 4 when r = 2. For any other positive r value, the area and circumference will be different values.

So in short, if a friend says that the area of a circle is the same as its perimeter, then you can immediately conclude the radius is 2.

Side note: throughout all of this solution, I used the approximation pi = 3.14 though pi has more decimal digits

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