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:

$z=\frac{X-\mu}{\sigma}$

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:

$z=\frac{53.0-60.0}{4.0}=-\frac{7}{4}$

It then follows that:

$P(X<53)=P(z<-\frac{7}{4})$

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

$P(X<53)=P(z<-\frac{7}{4})=0.0401$

The answer is 0.0401.