# Probability problem - finding standard deviation and mean in a normal dist.

• Hamish Cruickshank
In summary, the conversation is about a person seeking help with a problem in their maths methods course. The problem involves finding the mean and standard deviation of heart rate increases in a university study. The person mentions using a graphics calculator for this type of problem and eventually solves it on their own by using z scores and simultaneous equations. They provide their solution for future reference.
Hamish Cruickshank
Hey all.

Im doing maths methods 5 (i live in Australia) and I've run into this problem.
Code:
A university study investigated the increase in
heart rates(measured in beats per minute) of
people undertaking a particular exercise. The
increases in heart rate were normally distributed
with a mean of 40 and a standard deviation of 9.

It was determined that the proportion of people
classified as unfit (x >= 50) is 15% and the
proportion of people classified as very fit (x <= 22) is 10%.
Find the mean and standard deviation of the increases
in heart rate for this university study.

I've no idea how to do this.

Most of these types of problems I have been doing on a graphics calculator, which is allowed and expected in this course. The model of calculator I have is a CASIO fx-9860G AU.

Any help in solving this problem will be greatly appreciated.

Its okay, I got it figured out.

I took the z scores for those percentages as if they were standard normal distributions and then substituted them into the formula z = (x - mu)/sigma. I then had simultaneous equations which were quite easy to solve. I thought i'd answer my own question for anyone who wanted future reference.

## 1. What is the formula for finding the standard deviation in a normal distribution?

The formula for finding the standard deviation in a normal distribution is the square root of the variance, where the variance is the average of the squared differences from the mean.

## 2. How do you find the mean in a normal distribution?

The mean in a normal distribution is also known as the average or the central tendency. It can be found by adding all the values in the distribution and dividing by the total number of values.

## 3. Why is the standard deviation important in a normal distribution?

The standard deviation is important because it measures the spread or variability of the data from the mean in a normal distribution. It helps to understand how far away the data points are from the mean and how likely it is for a new data point to fall within a certain range.

## 4. Can the standard deviation be negative?

No, the standard deviation cannot be negative. It is always a positive value because it is the square root of the variance, which is the sum of squared differences from the mean.

## 5. How is the standard deviation related to the normal curve?

The standard deviation is closely related to the normal curve. In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. This creates the characteristic bell-shaped curve of the normal distribution.

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