Question

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≥ 75) is:a. 0.500b. 0.250c. 0.125d. 0.975e. 0.625

Answer 1

Answer:

a. 0.5

Step-by-step explanation:

We know that X follows normal distribution with

mean=75

standard deviation=8

$P(X\geq 75)=P(\frac{x-mean}{standard deviation}\geq \frac{75-75}{8})$

$P(X\geq 75)=P(Z\geq 0)$

$P(Z\geq 0)=$P(0<Z<∞)

The area under the normal curve is 1 and the  (0<Z<∞) =0.5 and (-∞<Z<0) =0.5

So, P(0<Z<∞)=0.5

Hence the P(X ≥ 75)=0.5