In variables estimation sampling, the sample standard deviation is used to calculate the?

1 answer:

3 0

The sample standard deviation is used to calculate the determine the spread of estimates for a set of observations (i.e., a data set) from the mean (average or expected value).

<h3>What is sample standard deviation?</h3>

The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured.

The sample standard deviation (s) is a measurement of the variation from the expected values and is equal to the sample variance's square root.

where

s = sample standard deviation

N = the number of observations

$xi$ = the observed values of a sample item

$\overline {x}$ = the mean value of the observations

Learn more about simple standard deviation, refer:

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A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount

-Dominant- [34]

Answer:

The company should use a mean of 12.37 ounces.

Step-by-step explanation:

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.

The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.17 ounce.

This means that $\sigma = 0.17$

The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)?

This is $\mu$ , considering that when $X = 12$ , Z has a p-value of $1 - 0.985 = 0.015$ , so when $X = 12, Z = -2.17$ .