Evaluate 2-(-4)+3+(-6)-(-2)

The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation

Bumek [7]

Answer:

0.7780

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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.

Population:

We have that $\mu = 7.19, \sigma = 0.86$

Sample of 12:

$n = 12, s = \frac{0.86}{\sqrt{12}} = 0.2483$

What is the probability that the mean cost will be more than $7.00?

This is 1 subtracted by the pvalue of Z when X = 7. So

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

By the Central Limit Theorem

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

$Z = \frac{7 - 7.19}{0.2483}$

$Z = -0.765$

$Z = -0.765$ has a pvalue of 0.222

1 - 0.222 = 0.778

So the answer is 0.7780

6 0

3 years ago

At what position on the number line is the red dot located?

Naddik [55]

Answer:

D. $\sqrt{46}$

Step-by-step explanation:

Firstly, we know it's close to 6.75, so we can compute 6.75*6.75 and the product should be close to whatever's under the $\sqrt$ . 6.75*6.75 = 45.5625, so we can already answer.