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dolphi86 [110]
3 years ago
5

Find the distance between each pair of points

Mathematics
1 answer:
torisob [31]3 years ago
7 0
Ok queued can be the 7
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The score on an exam from a certain MAT 112 class, X, is normally distributed with μ=78.1 and σ=10.8.
salantis [7]

a) X

b) 0.1539

c) 0.1539

d) 0.6922

Step-by-step explanation:

a)

In this problem, the score on the exam is normally distributed with the following parameters:

\mu=78.1 (mean)

\sigma = 10.8 (standard deviation)

We call X the name of the variable (the score obtained in the exam).

Therefore, the event "a student obtains a score less than 67.1) means that the variable X has a value less than 67.1. Mathematically, this means that we are asking for:

X

And the probability for this to occur can be written as:

p(X

b)

To find the probability of X to be less than 67.1, we have to calculate the area under the standardized normal distribution (so, with mean 0 and standard deviation 1) between z=-\infty and z=Z, where Z is the z-score corresponding to X = 67.1 on the s tandardized normal distribution.

The z-score corresponding to 67.1 is:

Z=\frac{67.1-\mu}{\sigma}=\frac{67.1-78.1}{10.8}=-1.02

Therefore, the probability that X < 67.1 is equal to the probability that z < -1.02 on the standardized normal distribution:

p(X

And by looking at the z-score tables, we find that this probability is:

p(z

And so,

p(X

c)

Here we want to find the probability that a randomly chosen score is greater than 89.1, so

p(X>89.1)

First of all, we have to calculate the z-score corresponding to this value of X, which is:

Z=\frac{89.1-\mu}{\sigma}=\frac{89.1-78.1}{10.8}=1.02

Then we notice that the z-score tables give only the area on the left of the values on the left of the mean (0), so we have to use the following symmetry property:

p(z>1.02) =p(z

Because the normal distribution is symmetric.

But from part b) we know that

p(z

Therefore:

p(X>89.1)=p(z>1.02)=0.1539

d)

Here we want to find the probability that the randomly chosen score is between 67.1 and 89.1, which can be written as

p(67.1

Or also as

p(67.1

Since the overall probability under the whole distribution must be 1.

From part b) and c) we know that:

p(X

p(X>89.1)=0.1539

Therefore, here we find immediately than:

p(67.1

7 0
3 years ago
The area of a square is given by x2, where x is the length of one side. Mary's original garden was in the shape of a square. She
Vinil7 [7]

Answer:

128\text{ ft}^{2}

Step-by-step explanation:

We have been given that the area of a square is given by x^2, where x is the length of one side.

Mary's original garden was in the shape of a square. She has decided to double the area of her garden. So the new area of Mary's garden will be 2 times the area of original garden.

We can represent this information in an equation as:

\text{Area of Mary's new garden}=2x^{2}

Therefore, the expression 2x^2 will represent the area of Mary's new garden.

To evaluate the area of new garden, if the side length of Mary's original garden was 8 feet, we will substitute x equals 8 in our expression.

\text{Area of Mary's new garden}=2(8\text{ ft})^{2}

\text{Area of Mary's new garden}=2*64\text{ ft}^{2}

\text{Area of Mary's new garden}=128\text{ ft}^{2}

Therefore, the area of Mary's new garden will be 128 square feet.

4 0
3 years ago
Me please I don’t understand
irakobra [83]
9 + 4 = 13

She is 13 floors away
8 0
2 years ago
Read 2 more answers
Michael is going to invest $15,000 into two savings accounts to save money to buy a house.
levacccp [35]

Answer:

Bank of Texas = $10,031.35

United Texas Bank = $10,500.00

Step-by-step explanation:

Bank of Texas

A=P(1+rt)

P=$7,500

r=6.75%

t=5 years

$10,031.35

refer the pic

United Texas Bank

A=P(1+rt)

P=$7,500

r=8%

t=5 years

$10,500.00

refer the sec pic

6 0
2 years ago
John has $20.43 dollars in his pocket. He buys a tv for $15.39 dollars. How many dollars does John have left?
AleksAgata [21]
All you do is subtract what John is spending from the amount he has. 20.43-15.39= $5.04
4 0
3 years ago
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