What is a zero of the problem
1 answer:
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Answer:
a) 0.2087 = 20.82% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.
b) 0.1834 = 18.34% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.
c) 0.3575 = 35.75% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they have very little confidence in newspapers, or they do not. The answers of each adult are independent, which means that the binomial probability distribution is used 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.
41% of U.S. adults have very little confidence in newspapers.
This means that
You randomly select 10 U.S. adults.
This means that
(a) exactly five
This is . So
0.2087 = 20.82% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.
(b) at least six
This is:
Then
0.1834 = 18.34% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.
(c) less than four.
This is:
So
0.3575 = 35.75% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.
Answer:
There is a probability of P=0.94 that at least 81 rolls are needed to get the sum of 307.
Step-by-step explanation:
The roll of a six-sided die sum has this parameters:
Mean: 3.5
Standard deviation: 1.7
If the die is rolled 81 times, the distribution of the sum of the 81 rolls will have the following parameters:
Note: the variance of the sum of random variables is equal to the sum of the variance of the individual variables.
Then, we can calculate the probabilties that the sum of 81 rolls is lower than 307.
There is 94% of chances that the sum of 81 rolls is lower than 307, so there is a probability of P=0.94 that at least 81 rolls are needed to get the sum of 307.