Mathematics, 23.03.2021 04:50 varonadestiny1109

2. Select the correct answer.

The national apple growers organization recently released its first crop of a new apple variety. It gathered data on the weight of the new apples.

It found a population mean of 4.85 ounces and a standard deviation of 0.92. Each sample size was 500 apples. By the central limit theorem,

which interval do 99.7% of the sample means fall within?

OA.

4.81 and 4.89

OB.

4.73 and 4.97

Ос. .

4.84 and 4.86

OD

4.77 and 4.93

Answers: 3

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Answers

Answer from: shelseamorrrow2411

B. 4.73 and 4.97

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

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.

Central Limit Theorem

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

Standard deviation of 0.92, sample of 500:

This means that $\sigma = 0.92, n = 500, s = \frac{0.92}{\sqrt{500}} = 0.04$

By the central limit theorem, which interval do 99.7% of the sample means fall within?

Within 3 standard deviations of the mean. So

4.85 - 3*0.04 = 4.85 - 0.12 = 4.73

4.85 + 3*0.04 = 4.85 + 0.12 = 4.97

So, option B.

Answer from: TaraC

4.73 and 4.97

Please give me brainliest, I really need it.

2.

Select the correct answer.
The national apple growers organization recently released its first c

Answer from: Quest

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead

Answer from: Quest

There is 240 red cars and there is 400 blue cars because 240/3=80 and 80*5=400

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The national apple growers organization recently released...