question archive Read Analyze and solve the following problems
Read Analyze and solve the following problems
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Read Analyze and solve the following problems. 5 points each item.
Use a bond paper or whole pad paper to show your computation.
Use this format to earn points credit in each item.
a. Given
b. Formula and substitution
c. Solution
d. Answer.
- A six-sided die is rolled 12 times. What is the probability of getting a 4 five times?
- A multiple choice test contains 20 questions with answer choices A,B,C and D. Only one answer choice to each question represent a correct answer. Find the probability that a student will answer exactly 6 questions correct if he makes random guesses on all 20 questions.
- 25% of all students enrolled in high school XYZ are taking Algebra. 30 students are chosen at random.
(a) Find the probability that exactly 7 students out of the 30-chosen are taking Algebra.
(b) What is the probability that fewer than 5 students out of the 30 who are selected are taking Algebra?
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Answer Preview
1. 2.84%
2. 16.86%
3.
a. 16.62%
b. 9.79%
Step-by-step explanation
1.
Given
p = 1/6
n = 12
x = 5
Formula and Substitution
P(X=x)=n?Cx?px(1−p)n−x
P(X=5)=12?C5?(61?)5(1−61?)12−5
Solution
P(X=5)=(792)(61?)5(65?)7=0.0284
Answer
P(X=5) = 2.84%
2.
Given
p = 1/4
n = 20
x = 6
Formula and Substitution
P(X=x)=n?Cx?px(1−p)n−x
P(X=6)=20?C6?(41?)6(1−41?)20−6
Solution
P(X=6)=(38760)(41?)6(43?)14=0.1686
Answer
P(X=6) = 16.86%
3.
(a)
Given
p = 0.25
n = 30
x = 7
Formula and Substitution
P(X=x)=n?Cx?px(1−p)n−x
P(X=7)=30?C7?(0.25)6(1−0.25)30−7
Solution
P(X=7)=(2035800)(0.25)7(0.75)23=0.1662
Answer
P(X=7) = 16.62%
(b)
Given
p = 0.25
n = 30
x < 5
Formula and Substitution
P(X<x)=∑x=0k?n?Cx?px(1−p)n−x
P(X<5)=∑x=04?30?Cx?(0.25)x(1−0.25)30−x
Solution
P(X<5)=∑x=04?30?Cx?(0.25)x(0.75)30−x=0.0979
Answer
P(X<5) = 9.79%
