Assume the random variable x is normally distributed with mean mu equals 50 μ=50 and standard ...

Explanation:

We must standardise the Random Variable \(X\) with the Standardised Normal Distribution \(Z\) variable using the relationship:

\(Z=\frac{\left(X-\mu \right)}{\sigma }\)

And we will use Normal Distribution Tables of the function:

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

And so we get:

\(P(X>35)=P\left(Z>\frac{35-50}{7}\right)\)

\(=P\left(Z>-2.1428\right)\)

So:

\(P\left(X>35\right)=P\left(Z>-2.1428\right)\)

From the table, -2.1428 is 0.0162, therefore:

Since we want when x is GREATER than 35, they're asking to the RIGHT of the filled in distribution, so subtract

1 - 0.0162 = 0.9838