According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 154 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees?

Answers

Answer 1

Answer:

Using the normal probability distribution and the central limit theorem, it is found that there is a 0.0869 = 8.69% probability that more than 20% of this sample is comprised of female employees.

Normal Probability Distribution

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

$Z = (X - \mu)/(\sigma)$

It 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, which is the percentile of X.

By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{(p(1 - p))/(n)}$ , as long as $np \geq 10$ and $n(1 - p) \geq 10$ .

In this problem:

16% of executive officers were women with companies that have company headquarters in the Midwest, hence p = 0.16.

A random sample of 154 executive officers from these companies was selected, hence n = 154.

The mean and the standard error are given by:

$\mu = p = 0.16$

$s = \sqrt{(p(1 - p))/(n)} = \sqrt{(0.16(0.84))/(154)} = 0.0295$

The probability that more than 20% of this sample is comprised of female employees is 1 subtracted by the p-value of Z when X = 0.2, hence:

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (0.2 - 0.16)/(0.0295)$

$Z = 1.36$

$Z = 1.36$ has a p-value of 0.9131.

1 - 0.9131 = 0.0869.

0.0869 = 8.69% probability that more than 20% of this sample is comprised of female employees.

To learn more about the normal probability distribution and the central limit theorem, you can take a look at brainly.com/question/24663213

Answer 2

Answer:

Answer: 0.0885

Step-by-step explanation:

Given : According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest.

i.e. p= 0.16

Sample size : n= 154

Now, the probability that more than 20% of this sample is comprised of female employees is given by :-

$P(p>0.20)=P(z>\frac{0.20-0.16}{\sqrt{(0.16(1-0.16))/(154)}})$

[∵ $z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}$ ]

$=P(z>1.35)\approx1-P(z\leq1.35)=1-0.9115=0.0885$ [Using the standard z-value table]

Hence, the required probability = 0.0885

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Help PLSSSSSSSSSSSSSSSSS extra points

Answers

Answer:

85 messages

Step-by-step explanation:

The system of equations for this is

35 + .10x

18 + .3x

where x = the number of text messages

Usually, you would use substitution or elimination to solve this problem. However, because the answer choices were given, you can just plug in the values.

When you plug in 85, or x = 85, you get 43.5 for both equations because

35 + .10(85) = 43.5 18 + .3(85) = 43.5

Therefore, the answer would be 85 messages becuase both plans will cost the same when you send 85 text messages!

Need help please show how you did it.

Answers

Answer:

(0, 1).

Method 1 (Substitution):

Substituting our two y's, we get the following:

$x^2 + 5x + 1 = x^2 + 2x + 1 \Rightarrow 3x = 0 \Rightarrow x = 0$

Thus, the only set of solutions is (0, 1). A quick sketch (either by hand or on Desmos) can confirm this.

Method 2 (Elimination):

We have two equations. We'll let the top one be equation 1 and the bottom one be equation 2. Eliminating as many variables as we can, we subtract (2) from (1) to get:

0 = 3x => x = 0.

So the only set of solutions is (0, 1).

Method 3 (Gaussian elimination):

We can place this in an augmented matrix and row reduce.

$\left[\begin{array}{cccc}1&5&1 & 1\n1&2&1 & 1\end{array}\right]$

Row reducing this gives us:

$\left[\begin{array}{cccc}1&5&1 & 1\n0&3&0 & 0\end{array}\right]$

This tells us that the only solution for x is x = 0 (since we read this as "3x = 0") and thus, the only solution we get is (0, 1).

3 gallons of paint cover 900 square feet. How many gallons will cover
1950 square feet?

Answers

Answer:

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Step-by-step explanation:

if 3g = 900

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A rectangular. Garden bed measures 8 x 6 feet a water faucet is at one corner of the bed hose must be long enough to reach opposite corner when stretched straight. Find required length of hose

Answers

Answer:

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Step-by-step explanation:

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8^2 = 64 and 6^2 = 36

64 + 36 = 100.

the square root of 100 is 10 so the length of the hose is `10.

Jake bought 4.08 pounds of apples he then bought 2.19 pounds of oranges how many pounds of fruit did he buy altogether? (SHOW YOUR WORK) place value charts (ONES).(TENTHS) (HUNDREDTHS) (THOUSANDS) also please dont give wrong answers im bad at math ❤️

Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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