Question

A continous random variable x is normally distributed with a mean of 56.3 and standard deviation of 7.2 illustrate a normal curve and find its probability
please help po​

Answer 1

Answer:

Explanation:

We must standardise the Random Variable #X# with the Standardised Normal Distribution #Z# Variable using the relationship:

# Z=(X-mu)/sigma #

And we will use Normal Distribution Tables of the function:

# Phi(z) = P(Z le z) #

And so we get:

# P(X>42) = P( Z > (42-50)/7 ) #

# " " = P( Z > -8/7 ) #

# " " = P( Z > -1.1429 ) #

If we look at this graphically it is the shaded part of this Standardised Normal Distribution:

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By symmetry of the Standardised Normal Distribution it is the same as this shaded part

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So;

# P(X>42) = P( Z > -1.1429 ) #

# " " = 1- P( Z < 1.1429 ) #

# " " = 1-Phi(1.1429 ) #

# " " = 1-0.8729 \ \ \ \ \ # (from tables)

# " " = 0.1271 #

Answer 2

Answer:

Explanation:

We must standardise the Random Variable X with the Standardised Normal Distribution Z Variable using the relationship:

Z=X−μσ

And we will use Normal Distribution Tables of the function:

Φ(z)=P(Z≤z)