In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples
1 answer:
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Answer:
a) 0.0000001024 probability that he will answer all questions correctly.
b) 0.1074 = 10.74% probability that he will answer all questions incorrectly
c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Each question has five answers, of which only one is correct
This means that the probability of correctly answering a question guessing is
10 questions.
This means that
A) What is the probability that he will answer all questions correctly?
This is
0.0000001024 probability that he will answer all questions correctly.
B) What is the probability that he will answer all questions incorrectly?
None correctly, so
0.1074 = 10.74% probability that he will answer all questions incorrectly
C) What is the probability that he will answer at least one of the questions correctly?
This is
Since , from item b.
0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
D) What is the probability that Richard will answer at least half the questions correctly?
This is
In which
So
0.0328 = 3.28% probability that Richard will answer at least half the questions correctly