Mathematics, 05.05.2020 18:18 jaydenromero31

Question 15
.
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

Answers: 1

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Answers

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.

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Answer from: xxaurorabluexx

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 from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

Answer from: Quest

step-by-step explanation:

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