Let us draw a triangle ABC with A=15° ,B=113° and b=7.
Please see the attached image.
We know that the sum of interior angles of a triangle is 180 degrees. Thus, we have
Apply Sine rule in the triangle ABC, we get
Therefore, we have
2b+15
2 dollars for each book so you multiply it by the number of books and add 15 because it is a one time fee.
Answer:
- In a cluster sample, every sample of size n has an equal chance of being included.
- In a stratified sample, random samples from each strata are included.
- In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
- In a stratified sample, every sample of size n has an equal chance of being included
Step-by-step explanation:
In a stratified sample the population is divided into different segments and then we take random elements from each segment.
In a cluster sample, the sample is divided into segments (or clusters) and then the sample is taken by selecting different clusters.
Therefore, in the cluster sample we take ALL elements from different clusters while in a stratified sample we take SOME elements from the different sections.
Now let's take a look at the options given:
- In a cluster sample, the only samples possible are those including every kth item from the random starting position: FALSE. In the cluster sample we select all items from the cluster.
- In a cluster sample, every sample of size n has an equal chance of being included: TRUE. if we divide the sample into clusters of size n then every cluster has an equal chance of being selected (since we select them at random).
- In a stratified sample, random samples from each strata are included: TRUE. We already said that we take a random sample from each segment (strata).
- In a stratified sample, the only samples possible are those including every kth item from the random starting position: FALSE. We can apply different methods to select our sample from each strata.
- In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included. TRUE. This is the definition of cluster sample we wrote at first.
- In a stratified sample, every sample of size n has an equal chance of being included: TRUE, we take samples from elements, not from stratas.
- In a cluster sample, random samples from each strata are included: FALSE. This is the definition of stratified sample.
- In a stratified sample, the clusters to be included are selected at random and then all members of each selected cluster are included: FALSE. This is the definition of cluster sample.
Since each trial has the same probability of success,
Let, <span><span><span>Xi</span>=1</span></span> if the <span><span>i<span>th</span></span></span> trial is a success (<span>0</span> otherwise). Then, <span><span>X=<span>∑3<span>i=1</span></span><span>Xi</span></span><span>X=<span>∑<span>i=1</span>3</span><span>Xi</span></span></span>,
and <span><span>E[X]=E[<span>∑3<span>i=1</span></span><span>Xi</span>]=<span>∑3<span>i=1</span></span>E[<span>Xi</span>]=<span>∑3<span>i=1</span></span>p=3p=1.8</span><span>E[X]=E[<span>∑<span>i=1</span>3</span><span>Xi</span>]=<span>∑<span>i=1</span>3</span>E[<span>Xi</span>]=<span>∑<span>i=1</span>3</span>p=3p=1.8</span></span>
So, <span><span>p=0.6</span><span>p=0.6</span></span>, and <span><span>P{X=3}=<span>0.63</span></span><span>P{X=3}=<span>0.63</span></span></span>
I thought what I did was sound, but the textbook says the answer to (a) is <span>0.60.6</span> and (b) is <span>00</span>.
Their reasoning (for (a)) is as follows:
