SCIENCE QUESTION BUT I HAD TO PUT IN MATH - I WILL GIVE BRAINLIEST TO CORRECT ANSWER

Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from rene

Veronika [31]

Answer:

99% of the sample means will fall between 0.93288 and 0.94112.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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.

The true mean is .9370 with a standard deviation of 0.0090

This means that $\mu = 0.9370, \sigma = 0.0090$

Sample of 32:

This means that $n = 32, s = \frac{0.009}{32} = 0.0016$

Within what interval will 99 percent of the sample means fall?

Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$-2.575 = \frac{X - 0.9370}{0.0016}$

$X - 0.9370 = -2.575*0.0016$

$X = 0.93288$

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

$Z = \frac{X - \mu}{s}$

$2.575 = \frac{X - 0.9370}{0.0016}$

$X - 0.9370 = 2.575*0.0016$

$X = 0.94112$

99% of the sample means will fall between 0.93288 and 0.94112.

6 0

3 years ago

Solve the equation in the interval 0 to 2pi.

galben [10]

Answer:

You don't need to single out $\cos \theta$ to solve this question.

To solve:

$\begin{aligned}3 \cos 4 \theta & = -2\\\\\cos 4 \theta & = -\dfrac{2}{3}\\\\4 \theta & = \cos^{-1}\left( -\dfrac{2}{3\right)}\\\\\implies 4 \theta & =2.30053... \pm 2 \pi n, -2.30053...\pm 2 \pi n\\\\\theta & =\dfrac{2.30053...}{4} \pm \dfrac{\pi n}{2}, -\dfrac{2.30053...}{4}\pm \dfrac{\pi n}{2}\end{aligned}$