Which is bigger 5/8 or 0.58
1 answer:
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The confidence interval is
. This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.
To find the confidence interval, we first find the z-score associated with it:
Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.
We calculate the margin of error using
This means that the confidence interval is
The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85
To find the confidence interval, we first find the z-score associated with it:
Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.
We calculate the margin of error using
This means that the confidence interval is
The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85
Answer:
a) 0.2581
b) 0.4148
c) 17
Step-by-step explanation:
For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So 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.
In this problem we have that:
a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is when
. So
b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is when
So
So
c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.
The expected value of the binomial distribution is:
In this question, we have
So
The closest integer to 16.5 is 17.