Question

A consumer organization that evaluates new motorcycles customarily reports the number of major defects in each motorcycle examined. Let X denote the number of major defects in a randomly selected motorcycle of a certain type. Recall the cumulative density function, or "cdf", is a function for x that calculates the probability of the value x and all values below, F(x) = P(X≤x) .
The cdf of X is as follows:
x 0 1 2 3 4 5 6
F(x) 0.06 0.20 0.30 0.52 0.91 0.97 1
1. Calculate the following probabilities directly from the cdf: (Round to two decimal places.)
(a) F(2), that is, P(X ≤ 2)
(b) P(X > 3)
(c) P(2 ≤ X ≤ 5)
(d) P(2 < X < 5)

Answer 1

Answer:

a) F(2)=0.30

b)P(X>3)=0.7

c)P(2≤X≤5)=0.67

d)P(2<X<5)=0.71

Step-by-step explanation:

a) F(2)=P(X≤2)=0.30

F(2) is given in the probability distribution

b) P(X>3)=1-P(X≤2)=1-F(2)=1-0.3=0.7

P(X>3)=0.7

c)P(2≤X≤5)=?

As we know that P(a≤X≤b)=F(b)-F(a)=P(X≤b)-P(X≤a)

So,

P(2≤X≤5)=P(X≤5)-P(X≤2)=F(5)-F(2)=0.97-0.3=0.67

P(2≤X≤5)=0.67

d)P(2<X<5)=P(1≤X≤4)=P(X≤4)-P(X≤1)=F(4)-F(1)=0.91-0.2=0.71.

P(2<X<5)=0.71