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**Answer**

The percentage of data lying between values ** a **and

**is denoted$P(axb)$**

*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 $\frac{55.3-50}{10}=0.53$

$P(x<55.3)=P(z0.53)$

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

Thus $P(x<55.3)=P(z0.53)=70.19\%$

$=70.19\%$

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