The diameter of a circle is 16 units.<br> What is the radius of the circle?

n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. W

miskamm [114]

Answer:

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

Step-by-step explanation:

The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Approximation:

We have to use the mean and the standard deviation of the hypergeometric distribution, that is:

$\mu = \frac{nk}{N}$

$\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}$

In this question:

88 + 88 = 176 students, which means that $N = 176$

88 non-history majors, which means that $k = 88$

44 students are selected, which means that $n = 44$

Mean and standard deviation:

$\mu = \frac{44*88}{176} = 22$

$\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88$

What is the probability that at least 22 of the 44 students selected are non-history majors?

Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is $P(X \geq 22 - 0.5) = P(X \geq 21.5)$ , which is 1 subtracted by the p-value of Z when X = 21.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21.5 - 22}{2.88}$

$Z = -0.17$

$Z = -0.17$ has a p-value of 0.4325

1 - 0.4325 = 0.5675

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

4 0

3 years ago

Each year the local country club sponsors a tennis tournament. Plays starts with 128 participants. During each round, half of th

valkas [14]

Answer:

128 divided by 2 for 5 times is your answer enjoy my.kiddo

3 0

3 years ago

What is the simplified form of the following expression square root 1/121

iogann1982 [59]

When you multiply a fraction, you do the top and the bottom separately, right?

Since a square root is like the opposite of multiplying, you can think of the top and the bottom separately for this too!

First, let's start with the top. The square root of 1 is 1, so the numerator is 1.

Now, let's do the bottom. The square root of 121 is 11, so the denominator is 11.

So, the answer is D, 1/11. You can check your answer by squaring it, and getting 1/121.

Hope this helps!

8 0

4 years ago

If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the fo

Salsk061 [2.6K]

Answer:

3s

Step-by-step explanation:

the answer is 3 seconds

8 0

3 years ago

A certain club has 20 members. What is the ratio of the number of 5-member committees that can be formed from the members of the

MissTica

Answer:

C

Step-by-step explanation:

This is a combination question.

In the first instance, we select 5 from 20 and in the second case , we select 4 from 20.

The total number of ways to solve the first instance is 20C5 = 15504 ways

The total number of ways to solve the second instance is 20C4 = 4,845

The ratio of the first to the second scenario is 15,504/4,845 = 3.2 = 16 to 5

8 0

3 years ago

The diameter of a circle is 16 units. What is the radius of the circle?