The number of defects in a machine-made product is a random variable with the fo

Question

The number of defects in a machine-made product is a random variable with the following probability distribution:

X

P(x)

0

0.5

1

0.3

2

0.1

3

0.1

(a) Find the probability that there are no more than 2 defects in a product.

(b) Find the probability that the number of defects in a product is between 1 and 3, inclusive.

(c) Find the probability that a randomly selected product has at most 1 defect.

(d) Find the expected number of defects in a product.

(e) Find the variance of the number of defects in a product.

X

P(x)

0

0.5

1

0.3

2

0.1

3

0.1

Explanation / Answer

(a) Find the probability that there are no more than 2 defects in a product.
P(X<=2) = P( X=0) + P(X=1)+ P(X=2) = 0.5 + 0.3 + 0.1 = 0.9

(b) Find the probability that the number of defects in a product is between 1 and 3, inclusive.
P(1 <=X <=3) = P(X=1) + P(X=2)+(X=3) = 0.3 + 0.1 + 0.1 = 0.5

(c) Find the probability that a randomly selected product has at most 1 defect.
P(X<=1) = P(X=0)+P(X=1) = 0.5 + 0.3 = 0.8

(d) Find the expected number of defects in a product.

f=   1  
fx =   0.8  

Expected defects = Mean = = fx / f =   0.8  
Mean square = f x^2 / f =   1.6  
      
Varriance = (Mean square) - (Mean)^2      
      
Varriance = f x^2 - Mean^2 =   0.96  

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.5 0 0 0 1 0.3 0.3 1 0.3 2 0.1 0.2 4 0.4 3 0.1 0.3 9 0.9

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.