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StatisticsQ&A Library1. A random variable Z that is normally distributed with mean0 and standard deviation o = 1 is said to have the2. The notation z is the z-score such that the area under thestandard normal curve to the right of za is3. IfX is a normal random variable with mean 40 and standarddeviation 10 and P(X> 45) = 0.3085, then P(X< 35)4. If X is normal random variable with mean 40 and standarddeviation 10 and P(X < 38) = 0.4207, then P(X= 38) =Question

Asked Oct 11, 2019

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question 1-4

Step 1

A **standard normal distribution** is normally distributed with mean µ = 0 and standard deviation σ = 1

1)

A random variable Z that is normally distributed with mean µ = 0 and standard deviation σ = is said to have the **Standard Normal Distribution**

2) The notation Z_{α} is the z-score such that the area under the standard normal curve to the right of Z_{α} is **1- α**

Here total area is 1, area to the left is **α**

**So, Total area to the right is 1- α**

3)

As per the question

Mean = 40

Standard deviation = 10

P(X>45) = 0.3085

P(X>40) = 0.5

P(40<X<45)= 0.5 – 0.3085 = 0.1915

P(X<40) = 0.5

P(35<X<40) = P(40<X<45) = 0.1915 (Because Normal distribution table is symmetrically distributed)

P(X<35) = P(X<40)- P(35<X<40) = 0.5 – 0.1915 = **0.3085**

**It is clearly shown in the table below**

Step 2

4)

In continuous rando...

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