Normal distribution percentages

Answer

The percentage of data lying between values a and b is denoted$P (a < x < b)$

The P in this inequality represents the probability or proportion.

On calculating the Normal Distrinution Percentages, we use the z-values.

We have previously learnt how to compute z values 

Notably, the process of computing the z-score is called standartization.

For example, consider a distribution N(50,10). The z-score of 55.3 is $\frac{55.3-50}{10}=0.53$

Finding the percentages

In computing the percentages under a normal distribution, one has to standardize every value.

for instance, finding$P(x<a)$ in the normal distribution $N(\mu ,\delta )$,

Step 1: one has to standardize a to $\frac{a-\mu }{\delta }$

Step 2: It involves calculating $P(z<\frac{a-\mu }{\delta })$

Step 3: Look up for the value of $\frac{a-\mu }{\delta }$ in the standard normal tables

Using the example above $\frac{55.3-50}{10}=0.53$

$P(x<55.3)= P(z<0.53)$

Upon looking up for the value of 0.53 in the standard table. The value is 0.7019.

Thus $P(x<55.3)= P(z<0.53)= 70.19\%$

$=70.19\%$

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