-aux.06.normal distribution to standard distribution

In summary, the normal distribution and standard distribution are both types of continuous probability distributions. The standard distribution is a standardized version of the normal distribution with a mean of 0 and a standard deviation of 1. To convert from a normal distribution to a standard distribution, the mean is subtracted from each value and then divided by the standard deviation. This allows for easier comparison and use of standard statistical methods. However, the data should follow a roughly normal distribution for the conversion to be meaningful, and there may be limitations such as distorted data or the assumption of normality.
  • #1
karush
Gold Member
MHB
3,269
5
so for (a) (i) I used $\frac{x-\mu}{\sigma}=z
$\dfrac{0.70-0.76}{0.06}=-1 = a $ and $\frac{0.79-0.76}{0.06}=.5 = b$
ii $P(.70<X)$ z-table for $-1$ is $0.3413$ so $0.3413 + .500 = 0.8413$
$P(.70<X<.79)$ z-table for $.5$ is $0.1915$ so $0.3413+0.1915=0.5328$
 
Last edited:
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  • #2
Looks good so far! (Sun)
 
  • #3
(b) (i)
View attachment 1139

(ii) z-table for $3\% \approx -1.88$

so $\frac{c-0.76}{0.06}=-1.88$ thus $c\approx 0.65 s$

my shaky attempt at this anyway(Wasntme)
 
  • #4
Again, looks good! (Clapping)
 
  • #5
MarkFL said:
Again, looks good! (Clapping)

well, it definitely pays to ask for help...:cool:
 

FAQ: -aux.06.normal distribution to standard distribution

1. What is the difference between normal distribution and standard distribution?

The normal distribution is a continuous probability distribution that represents the distribution of a population's values and is often referred to as a "bell curve." The standard distribution is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. In other words, the standard distribution is a standardized version of the normal distribution.

2. How do you convert from normal distribution to standard distribution?

To convert from a normal distribution to a standard distribution, you need to subtract the mean from each value and then divide by the standard deviation. This process is known as standardizing or normalizing the data.

3. What is the purpose of converting to standard distribution?

Converting to standard distribution allows for easier comparison and interpretation of data. It also allows for the use of standard statistical methods and assumptions, such as using z-scores to calculate probabilities and making inferences about the population.

4. Can any data set be converted to standard distribution?

Technically, yes. However, in order for the conversion to be meaningful, the data should follow a roughly normal distribution. If the data is heavily skewed or has extreme outliers, converting to standard distribution may not be appropriate.

5. Are there any limitations to using standard distribution?

One limitation of using standard distribution is that it assumes the data follows a normal distribution, which is not always the case in real-world scenarios. Additionally, the conversion process can sometimes distort the data, especially if the sample size is small.

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