SaiBook.us Statistics

Home Course Section

Register Enroll Refer

Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Binomial distribution

Grade: 9-a Lesson: S4-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	The random variable X has binomial distribution B(6,0.4). Determine each of the following. a) P(X≥4) b) P(X<2).?
2	Formula:	Probability P(x)=\$n_(C_x) p^x q^(n-x)\$
3	Step	From the given data	n= 20,p=0.4
4	Step	Finding the value of q	q = 1-p q = 1-0.4 ⇒ q=0.6
5	Step	P(X≥4)	P(x=4) + P(x=5) + P(x=6)
6	Step	Substitute all the values in P(X≥4)	\$6_(C_4)(0.4)^4(0.6)^(6-4) + 6_(C_5)(0.4)^5(0.6)^(6-5) + 6_(C_6)(0.4)^6(0.6)^(6-6)\$
7	Hint	\$n_(C_x) = (n!)/((n-x)!x!)\$
8	Step	P(X≥4)	\$(6!)/((6-4)!4!) (0.4)^4 (0.6)^4 + (6!)/((6-5)!5!) (0.4)^5 (0.6)^5 +(6!)/((6-6)!6!) (0.4)^6 (0.6)^6\$
9	Step	Simplification P(X≥4)	\$(6!)/(2!4!)(0.4)^4 (0.6)^4 + (6!)/(1!5!)(0.4)^5 (0.6)^5 + (6!)/(0!6!)(0.4)^6 (0.6)^6\$
10	Step	After simplification	(15×0.0256×0.1296) + (6×0.0102×0.0777) + (1×0.0040×0.0466)
11	Step	P(X≥4)	0.0497 + 0.0475 + 0.0001
12	Step	P(X≥4)	0.0973
13	Step	P(X<2)	P(x=1) + P(x=0)
14	Step	Substitute all the values in P(X<2)	\$6_(C_1)(0.4)^1(0.6)^(6-1) + 6_(C_0)(0.4)^0(0.6)^(6-0)\$
15	Step	Simplification P(X<2)	\$(6!)/((6-1)!1!) (0.4)^1 (0.6)^1 + (6!)/((6-0)!0!) (0.4)^0 (0.6)^0\$
16	Step	Simplification	P(X<2) = \$(6!)/(5!1!)(0.4)^1 (0.6)^1 + (6!)/(6!0!)(0.4)^0 (0.6)^0\$
17	Step	After simplification	(6×0.6×0.4) + (1×1×1)
18	Step	P(X<2)	1.44 + 1
19	Step	P(X<2)	2.44
20	Step	P(X≥4) = 0.0973 P(X<2) = 2.44
21		Answer	A

Step

Type

Explanation

Answer

Problem

The random variable X has binomial distribution B(6,0.4). Determine each of the following.
a) P(X≥4)
b) P(X<2).?

Formula:

Probability P(x)=\$n_(C_x) p^x q^(n-x)\$

Step

From the given data

n= 20,p=0.4

Step

Finding the value of q

q = 1-p

q = 1-0.4 ⇒ q=0.6

Step

P(X≥4)

P(x=4) + P(x=5) + P(x=6)

Step

Substitute all the values in P(X≥4)

\$6_(C_4)(0.4)^4(0.6)^(6-4) + 6_(C_5)(0.4)^5(0.6)^(6-5) + 6_(C_6)(0.4)^6(0.6)^(6-6)\$

Hint

\$n_(C_x) = (n!)/((n-x)!x!)\$

Step

P(X≥4)

\$(6!)/((6-4)!4!) (0.4)^4 (0.6)^4 + (6!)/((6-5)!5!) (0.4)^5 (0.6)^5 +(6!)/((6-6)!6!) (0.4)^6 (0.6)^6\$

Step

Simplification P(X≥4)

\$(6!)/(2!4!)(0.4)^4 (0.6)^4 + (6!)/(1!5!)(0.4)^5 (0.6)^5 + (6!)/(0!6!)(0.4)^6 (0.6)^6\$

Step

After simplification

(15×0.0256×0.1296) + (6×0.0102×0.0777) + (1×0.0040×0.0466)

Step

P(X≥4)

0.0497 + 0.0475 + 0.0001

Step

P(X≥4)

0.0973

Step

P(X<2)

P(x=1) + P(x=0)

Step

Substitute all the values in P(X<2)

\$6_(C_1)(0.4)^1(0.6)^(6-1) + 6_(C_0)(0.4)^0(0.6)^(6-0)\$

Step

Simplification P(X<2)

\$(6!)/((6-1)!1!) (0.4)^1 (0.6)^1 + (6!)/((6-0)!0!) (0.4)^0 (0.6)^0\$

Step

Simplification

P(X<2) = \$(6!)/(5!1!)(0.4)^1 (0.6)^1 + (6!)/(6!0!)(0.4)^0 (0.6)^0\$

Step

After simplification

(6×0.6×0.4) + (1×1×1)

Step

P(X<2)

1.44 + 1

Step

P(X<2)

2.44

Step

P(X≥4) = 0.0973
P(X<2) = 2.44

Answer

Tutor: Questions

Seq	Type	Question
1	Problem	What did you learn from this problem?
2	Clue	What did you learn from the clues?
3	Hint	What did you learn from the Hints?
4	Step	What did you learn from the Steps?
5	Step	How can we improve the Steps?

Seq

Type

Question

Audio

Problem

What did you learn from this problem?

Clue

What did you learn from the clues?

Hint

What did you learn from the Hints?

Step

What did you learn from the Steps?

Step

How can we improve the Steps?