Question

20. Assume that X has a normal distribution, and find the indicated probabilityThe mean is u - 60,0 and the standard deviation is o = 4.0,Find the probability that X is less than 53.0.

Answer 1

Recall that the Normal Distribution Formula is given by the z-score:

`z=(X-\mu)/(\sigma)`

Where μ is the mean and σ is the standard deviation.

Substitute μ=60.0, σ=4.0, and X=53.0 into the formula:

`z=(53.0-60.0)/(4.0)=-(7)/(4)`

It then follows that:

`P(X<53)=P(z<-(7)/(4))`

Next, check this in the normal distribution table, to get:

`P(X<53)=P(z<-(7)/(4))=0.0401`

The answer is 0.0401.