MATHEMATICS COLLEGE

A survey among students at a certain university revealed that the number of hours spent studying the week before final exams was approximately normally distributed with mean 25 and standard deviation 6. What proportion of students studied between 25 and 34 hours

Answers

Answer 1

Answer:

Answer:

$P(25<X<34)=P((25-\mu)/(\sigma)<(X-\mu)/(\sigma)<(34-\mu)/(\sigma))=P((25-25)/(6)<Z<(34-25)/(6))=P(0<z<1.5)$

And we can find this probability with this difference:

$P(0<z<1.5)=P(z<1.5)-P(z<0)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(0<z<1.5)=P(z<1.5)-P(z<0)=0.933-0.5=0.433$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem'

Let X the random variable that represent the hous spent studying the week before final exams of a population, and for this case we know the distribution for X is given by:

$X \sim N(25,6)$

Where $\mu=25$ and $\sigma=6$

We are interested on this probability

$P(25<X<34)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=(x-\mu)/(\sigma)$

If we apply this formula to our probability we got this:

$P(25<X<34)=P((25-\mu)/(\sigma)<(X-\mu)/(\sigma)<(34-\mu)/(\sigma))=P((25-25)/(6)<Z<(34-25)/(6))=P(0<z<1.5)$

And we can find this probability with this difference:

$P(0<z<1.5)=P(z<1.5)-P(z<0)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(0<z<1.5)=P(z<1.5)-P(z<0)=0.933-0.5=0.433$

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Order the following numbers from least to greatest

Answers

Answer:

Step-by-step explanation:

Change all numbers to their decimal form.

37.5 % = 37.5 / 100 = 0.375

1/3 = 0.3333

0.3 = 0.3

40% = 40/100 = 0.4

3/5 = 0.6

Order

0.3

0.33333

0.375

0.4

0.6

5/3 x − 10 = 1/3 x
What is the value of x?

Answers

Answer:

X=1.66666667 hope this hepled

Step-by-step explanation:

by simplifying both sides of the equation, then isolating the variable.
X =7.5

What is the volume of a cone with the given dimensions. radius=4 cm; height= 10 cm

Answers

167.552 the volume of a cone is piR^2h/3

Answer:

$167.47 \: {cm}^(3)$

Step-by-step explanation:

$V_(cone) = (1)/( 3) \pi {r}^(2)h \n \n = (1)/( 3) \pi * {4}^(2) * 10 \n \n = (1)/( 3) * 3.14 * 16 * 10 \n \n = (1)/( 3) * \: 502.4 \n \n = 167.466667 \n \n = 167.47 \: {cm}^(3)$

CAN SOMEONE HELP PLEASE ASAP!!! ILL MAKE YOU BRAINLIEST

Answers

Answer:

I think the answer is D but I'm not 100 percent sure. I hope this helps

Step-by-step explanation:

I think I took this test before

What is the result of adding these two equations?
5x-y=6
-2x+y=8

Answers

3x=14 I am pretty sure

Subtract. (29v)−(−13v+59)

Answers

The value of the equation is A = 42v - 59

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( 29v ) - ( -13v + 59 ) be equation (1)

On simplifying the equation , we get

A = 29v - ( -13v ) - 59

On further simplification , we get

A = 29v + 13v - 59

The value of A = 42v - 59

Therefore , the value of A is 42v - 59

Hence , the equation is A = 42v - 59