Question

for a continuous random variable x, p(25 ≤ x ≤ 72) = 0.16 and p(x > 72) = 0.21. calculate the following probabilities
note: round your answers to 2 decimal places.
a p(x < 72)
b p(x < 25)
c p(x = 72)

Explanation:

Step1: Calculate \(P(X < 72)\)

We know that \(P(X\geq72)=P(X > 72)\) (for continuous random variable). Also, \(P(X < 72)+P(X\geq72)=1\).
Since \(P(X > 72)=0.21\), then \(P(X < 72)=1 - P(X > 72)\)
\(P(X < 72)=1 - 0.21=0.79\)

Step2: Calculate \(P(X < 25)\)

We know that \(P(25\leq X\leq72)=0.16\) and \(P(X < 72)=0.79\).
Using the formula \(P(X < 25)+P(25\leq X\leq72)=P(X < 72)\)
So \(P(X < 25)=P(X < 72)-P(25\leq X\leq72)\)
\(P(X < 25)=0.79 - 0.16=0.63\)

Step3: Calculate \(P(X = 72)\)

For a continuous random variable \(X\), \(P(X = c)=0\) for any single - point \(c\). So \(P(X = 72)=0\)

Answer:

a. \(0.79\)
b. \(0.63\)
c. \(0\)