I need help simplifying problem 9 on practice
1 answer:
You might be interested in
Answer:
Answer: the probability is 0.13
Step-by-step explanation:
First, each question has 5 options and only one is correct.
Then, selecting at random, the probability of getting a correct answer is equal to:
p = 1/5 = 0.20 (and the probability of getting it incorrect is p = 4/5 = 0.80)
Now, if out of 30 questions, we got 4 correct and 26 incorrect, the probability for a given combination is;
p = (0.20^4)*(0.80^26)
But we also need to multiply this by the total number of combinations.
This is we have 30 questions in total, and we can select 4 of them that will be the correct ones.
Now, if we have N objects in total, the number of different combinations of K elements out of those N elements is
In this case, N = 30 and K = 4.
Then the probability of getting exactly 4 correct answers is:
P = (0.20^4)*(0.80^26)*27,405 = 0.13
Answer:
The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 1.645.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 40.5 - 1.2 = 39.3 hours
The upper end of the interval is the sample mean added to M. So it is 40.5 + 1.2 = 41.7 hours
The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.