# Mean and standard deviation and probability

• MHB
• tcardwe3
In summary, the conversation discusses the normal distribution of systolic blood pressure for women aged 18-24, with a mean of 114.8 and standard deviation of 13.1. It also mentions the calculation of mean and standard deviation for a sample of 100 women. The second part of the conversation introduces the concept of the sampling distribution of a normal variable, with a mean of $\mu$ and variance of $\frac{\sigma^2}{n}$. Using this information, the probability of the mean systolic blood pressure falling between 112.2 and 116.4 is discussed.
tcardwe3
I did the problem but none of my answers match up with the answer choices so I'm obviously doing it wrong. Can someone show me how to do these two problems. I have a test coming up and I am so behind

For women aged 18-24, the systolic blood pressure (in hg mm) are normally distributed with a mean of 114.8 and a standard deviation of 13.1
100 women between 18 and 24 are randomly selected, let t represent the systolic pressure of 100 women
-Find the mean and standard deviation of t
a) 114.8, 131
b) 114.8, 13.1
c) 114.8, 1.31
d) 11.48, 1.31
d) 11.48, 1.31

-What is the probability that the mean systolic blood pressure t is between 112.2 and 116.4
a) .8649
b) .3879
c) .1578
d) .571
e) .0324

[box=red]
Sampling Distribution of a Normal Variable

Given a random variable $$\displaystyle X$$. Suppose that the population distribution of $$\displaystyle X$$ is known to be normal, with mean $\mu$ and variance $\sigma^2$, that is, $X\sim N(\mu,\sigma)$. Then, for any sample size $n$, it follows that the sampling distribution of $X$ is normal, with mean $\mu$ and variance $\dfrac{\sigma^2}{n}$, that is, $\overline{X}\sim N\left(\mu,\dfrac{\sigma}{\sqrt{n}}\right)$[/box]

Based on this, what would you say the correct answer to the first part of the problem is?

For the second part of the question.

$\displaystyle P\left(112.2<\bar{T}<116.4\right) = P\left(\frac{112.2-\mu}{\frac{\sigma}{\sqrt{n}}}<Z<\frac{116.4-\mu}{\frac{\sigma}{\sqrt{n}}}\right)= \cdots$

## 1. What is the difference between mean and standard deviation?

The mean is the average value of a set of numbers, while the standard deviation is a measure of how spread out the numbers are from the mean. In other words, the mean tells us where the center of the data is, and the standard deviation tells us how much the data deviates from the mean.

## 2. How do you calculate mean and standard deviation?

To calculate the mean, add all of the numbers in a data set and divide by the total number of values. To calculate the standard deviation, first find the mean, then for each number in the data set, subtract the mean and square the result. Find the mean of these squared differences, and then take the square root of that value. This will give you the standard deviation.

## 3. What is the significance of probability in statistics?

Probability is a measure of the likelihood of an event occurring. In statistics, it is used to analyze and interpret data, make predictions, and determine the likelihood of certain outcomes. It is an essential tool for understanding and making decisions based on data.

## 4. How is probability related to mean and standard deviation?

In statistics, the probability of an event is often expressed as a proportion or percentage. Mean and standard deviation are used to describe the distribution of values within a data set. The mean and standard deviation can also be used to calculate the probability of a certain outcome occurring within a given data set.

## 5. How can mean and standard deviation be used to make predictions?

Mean and standard deviation can be used to make predictions by providing information about the central tendency and spread of a data set. This information can be used to estimate the likelihood of certain outcomes occurring and make informed decisions based on the data. Additionally, mean and standard deviation can be used to identify any outliers in the data that may affect the accuracy of predictions.

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