The members of an organization are 10 men and 11 women

You are collecting a sample of 60 data points from a population that you know to follow an exponential distribution. It is not a

11111nata11111 [884]

Answer:

For the exponential distribution:

$\mu = \frac{1}{\lambda}$

$\sigma^2 = \frac{1}{\lambda^2}$

We know that the exponential distribution is skewed but the sample mean for this case using a sample size of 60 would be approximately normal, so then we can conclude that if we have a sample size like this one and an exponential distribution we can approximate the sample mean to the noemal distribution and indeed use the Central Limit theorem.

$\bar X \sim N(\mu_{\bar X} , \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X} = \bar X$

$\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}$

Step-by-step explanation:

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

For this case we have a large sample size n =60 >30

The exponential distribution is the probability distribution that describes the time between events in a Poisson process.

For the exponential distribution:

$\mu = \frac{1}{\lambda}$

$\sigma^2 = \frac{1}{\lambda^2}$

We know that the exponential distribution is skewed but the sample mean for this case using a sample size of 60 would be approximately normal, so then we can conclude that if we have a sample size like this one and an exponential distribution we can approximate the sample mean to the noemal distribution and indeed use the Central Limit theorem.

$\bar X \sim N(\mu_{\bar X} , \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X} = \bar X$

$\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}$

5 0

4 years ago

Any one that knows this please help thanks!

rjkz [21]

The answer is -7/8 the alternative answer is 0.875

6 0

3 years ago

Lin's job pays $8.25 an hour plus $10 of transportation allowance each week. She has to work at least 5 hours a week to keep the

Usimov [2.4K]

Y=8.25x+10

10 is the allowance plus the 8.25 times x which is the hours

5 0

3 years ago

The population of Oregon is about 4,000,000. What is the order of magnitude of this number?

CaHeK987 [17]

The order of magnitude is the same thing as saying the scientific notation which is 4x10 to the power of six. The important thing about scientific notation is that there has to be a number only in the tens place but nothing in the hundreds and thousands.

8 0

4 years ago

David requires at least $300 to hold his birthday party. If David can save $63 a month, how many months will he need to save to

Darya [45]

Answer:

a. $63x \geq 300$

b. $x \geq 4.76$ $or$ $x\geq 5$

c. For David to achieve three hundred dollars, he would have to save approximately 5 months

Step-by-step explanation:

A. David requires three hundred dollars, this is his goal, indicating the three hundred must be alone. For the inequality sign, the statement says that he "requires at least $300", meaning that he would have to maintain three hundred dollars or his amount could go greater than $300. Therefore, the inequality sign should be "≥" or "greater than or equal to". We also know that David can save 63 dollars per month, meaning that there should be a variable next to 63 so we could replace "x" with any number to solve our inequality. This should leave us with the following inequality :

63x ≥ 300

B. To solve the inequality, we need to get x alone, to do so, divide 63 by both sides,

$\frac{63x}{63} \geq \frac{300}{63}$

$x \geq 4.76$

To make it easier, we can round "4.76" to 5.

$x \geq 5$

C. Already shown in the answer spot

4 0

3 years ago