Answer:
This test batch can be chosen in 2380 ways
Step-by-step explanation:
The order in which the batteries are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In how many ways can this test batch be chosen?
4 batteries from a set of 17. So
This test batch can be chosen in 2380 ways
Complete question is;
Given n objects are arranged in a row. A subset of these objects is called unfriendly, if no two of its elements are consecutive. Show that the number of unfriendly subsets of a k-element set is ( n−k+1 )
( k )
Answer:
I've been able to prove that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
Step-by-step explanation:
I've attached the proof that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
Answer:
The mean of the sampling distribution of means for the 36 students is of 18.6 homework hours per week.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
For the population, the mean is 18.6. So, by the Central Limit Theorem, the mean of the sampling distribution is also 18.6.
Answer:
And for this case the margin of error would be:
If the level of confidence increase we can conclude that the value of would increase and the the confidence interval would be wider, since the margin of error increase.
c. Increase; wider
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
Let's assume that we have a parameter of interest and we want to estimate the value of p with
and in general the confidence interval if the distribution of p is normal is given by:
And for this case the margin of error would be:
If the level of confidence increase we can conclude that the value of would increase and the the confidence interval would be wider, since the margin of error increase.
c. Increase; wider