Question

Question 15
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fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5
and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5
imes, and the mean of the 5 values landing face up is recorded.
The mean and standard deviation of the results of the simulation should be close to which of the following?
Mean 3.5 and standard deviation 1.7078
Mean 3.5 and standard deviation 0.7638
C) Mean 3.5 and standard deviation 0.0854
D
Mean 17.5 and standard deviation 1.7078
Mean 17.5 and standard deviation 0.7638

Answer 1

Answer:

The correct option is (C).

Step-by-step explanation:

According to the Central Limit Theorem if we have n unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample means is given by,

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

The information provided is:

μ = 3.5

σ = 1.7078

n = 400 = number of times the experiment is repeated.

As the sample size is quite large, i.e. n = 400 > 30 the central limit theorem can be used to approximate the sampling distribution of the sample mean.

The mean of the distribution of sample means is:

$\mu_{\bar x}=\mu=3.5$

The standard deviation of the distribution of sample mean is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{1.7078}{\sqrt{400}}=0.0854$

The distribution of the sample mean is:

$\bar X\sim N(\mu = 3.5,\ \sigma=0.0854)$.

Thus, the correct option is (C).

Answer 2

The mean of the distribution of sample means is 3.5 and the standard deviation of the distribution of sample means is 0.0854 and this can be determined by using the given data.

Given :

• Fair die has its faces numbered from 1 to 6.
• Let random variable F represent the number landing face up when the die is tossed.
• The probability distribution for the random variable has a mean of 3.5  and standard deviation 1.7078.
• Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die.
• For each trial, the die is tossed 5  times and the mean of the 5 values landing face-up is recorded.

The mean of the distribution of sample means is given by:

$\mu_{\bar{x}} = \mu = 3.5$             ----- (Given)

The standard deviation of the distribution of sample means is given by:

$\sigma_{\bar{x}} = \dfrac{\sigma }{\sqrt{n} }$

$\sigma_{\bar{x}}=\dfrac{1.7078}{\sqrt{400} }$

$\sigma_{\bar{x}}=0.0854$

So, the correct option is given by C) Mean 3.5 and standard deviation 0.0854.

For more information, refer to the link given below:

https://brainly.com/question/23017717