The mean and standard deviation of the x sampling distribution for each of the following sample sizes will be $N(100,10/\sqrt{41} ), N(100,10/\sqrt{130} )$ .

<h3>What is the distribution of the sample mean for large samples?</h3>

Suppose X has a distribution with mean $\mu$ and standard deviation $\sigma,$ then,

the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with a mean equal to the mean of X, and a standard deviation equal to $\sigma/\sqrt{n}$

Symbolically, we write it as:

$X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )$

A random sample is selected from a population with a mean = of 100 and a standard deviation = of 10.

The mean and standard deviation of the x sampling distribution for each of the following sample sizes.

If N=41

$X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{41} )$

If N=130

$X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{130} )$

Learn more about standard normal distribution here:

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8 0

3 years ago

A plumber has an 8-foot piece of cooper pipe. He needs to cut a 3-foot 10-inche piece of cooper pipe to repair a leak in a sink'

algol13

Answer:

50 inches

Step-by-step explanation:

Since you want the result in inches, you can convert both measures to inches before subtracting.

8 ft = 8 × 12 in = 96 in

3 ft = 3 × 12 in = 36 in

so 3 ft 10 in = 36 in + 10 in = 46 in

The amount of pipe remaining is ...

96 in - 46 in = 50 in

The plumber will have 50 inches of copper pipe left after the repair.

3 0

3 years ago

Which modified box plot represents the data set? 10, 12, 2, 4, 24, 2, 7, 7, 9

Ratling [72]

The fourth option is the answer. When graphed, Min is 2, Q1 is 3, Median is 7, Q3 is 11, and Max is 24. The fourth option is the one that follow all of those!

7 0

3 years ago

Read 2 more answers

Please hurry; The number of bacteria in a culture grows exponentially. It can be modeled with the function f(x) = 20 (2^x).

Amiraneli [1.4K]

Answer:

Step-by-step explanation:

20(2^6) = 1280

8 0

3 years ago