MATHEMATICS COLLEGE

Help!! Is anyone good at algebra??

Answers

Answer 1

Answer:

Answer:

h = 20 m

Step-by-step explanation:

So you know volume of a cylinder = π*(r^2) * h

and you also know volume of this cylinder = 180π

(volume is also in meters^3)

you can set these volumes equal to one another

180π = π*(r^2) * h

by dividing by π you get this:

180 = (r^2) * h

you need h so you can divide by r^2 to get this

h = 180 / (r^2)

now you just need to plug in the radius you are given which was 3 meters

h = 180 m^3 / (3 m^2)

h = 180 m^ 3 / 9 m^2

h = 20 m

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A final exam in Sociology has a mean of 72 and a standard deviation of 9.2. If 35 students are randomly selected, find the probability that that the mean of their test scores will be greater than 76. (Round to tenth of a percent)

Answers

Answer: 0.5%

Step-by-step explanation:

We assume that the test scores in final exam is normally distributed.

Given : Mean : $\mu= 72$

Standard deviation : $\sigma=9.2$

Sample size : n= 35

Let x be the random variable that represents the test scores of the students.

The formula for the z-score :-

$z=(x-\mu)/((\sigma)/(√(n)))$

For x=76

$z=(76-72)/((9.2)/(√(35)))\approx2.57$

By using the standard normal distribution table ,

The p-value = $P(x>76)=P(z>2.57)=1-P(z\leq2.57)$

$=1-0.994915=0.005085=0.5085\%\approx0.5\%$

Hence, the probability that that the mean of their test scores will be greater than76 =0.5%

Final answer:

The probability that the mean test score of 35 randomly selected Sociology students will be greater than 76 is 0.5%, calculated by using the Central Limit Theorem and the Z-score formula.

Explanation:

In Sociology, to find the probability that the mean of the test scores for a randomly selected group of 35 students will be greater than 76, we use the concepts of the Central Limit Theorem and the Z-score formual.

First, we calculate the standard error which is the standard deviation divided by the square root of the sample size (9.2/sqrt(35) which roughly equals 1.55).

Next, we calculate the Z-score which is the difference between the sample mean and population mean divided by the standard error (76-72)/1.55, which equals roughly 2.58.

Finally, by looking at the Z-table, we find that the area to the left of Z=2.58 is 0.9951, which means that the area to the right (representing the probability of a score >= 76) is 1 - 0.9951= 0.0049 or 0.5%. So the probability that the average test score of the randomly selected 35 students will be greater than 76 is 0.5%.

Learn more about Probability in Sociology here:

brainly.com/question/34209725

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