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3 years ago

6

We toss a die three times. Among all possible outcomes, how many have at least one occurrence of "6"?

1 answer:

zlopas [31]3 years ago

3 0

There are 6×6×6 = 216 possible outcomes. Of those, 5×5×5 = 125 of them will be outcomes that do not have any occurrences of 6. The number that will have at least one occurrence of 6 is 216 - 125 = 91.

_____

5×5×5 counts the number of ways that the numbers 1–5 might be rolled on 3 rolls.

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Art [367]

Answer:

b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal Variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:

This means that:

$\mu_G = 15$

$s_G = \frac{4.2}{\sqrt{35}} = 0.71$

The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Sample of 40:

This means that:

$\mu_E = 13.4$

$s_E = \frac{3.7}{\sqrt{40}} = 0.585$

Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?

Shape is approximately normal.

Mean:

$\mu = \mu_G - \mu_E = 15 - 13.4 = 1.6$

Standard deviation:

$s = \sqrt{s_G^2+s_E^2} = \sqrt{0.71^2+0.585^2} = 0.92$

So the correct answer is given by option b.

8 0

3 years ago

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3 years ago

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Answer:

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Step-by-step explanation:

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i dont know

3 0

3 years ago

A random sample has been selected from a population. The point estimate = 78.65 and margin of error E = 8.24 for a 90% confidenc

fiasKO [112]

Answer:

90% confidence interval: (70.41,86.89)

Step-by-step explanation:

We are given the following in the question:

Point estimate = 78.65

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Formula:

$\text{Point estimate} \pm \text{Margin of error}$

Putting the values, we get,

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Step-by-step explanation:

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3 years ago

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