Data Distribution Questions and Answers

An engineering company has four openings and the applicant pool consists of 6 database administrators and eight network engineers. All are equally qualified so the hiring will be done randomly. The hiring committee consists of 4 women and 4 men.
d. How many ways can 1 network engineers be chosen?
e. What is the probability that the random selection of the four persons to be hired will result in 3 database administrators and 1 network engineer?

Suppose you are a fan of baseball, which has two different leagues in the US, the National League and the American League. The winners of both the leagues play in the World Series Championship each year. You want to test whether both the leagues are equally strong, or whether one of the leagues is stronger than the other. Assume that each year the AL champion wins the world series with probability p, and the NL champions win with probability ${\displaystyle 1-p}$, where p is an unknown number in (0, 1).
Starting from 1903, the world series championship has been played 115 times, and the AL champions won it 66 times, and the NL champions won it 49 times. Based on this data, carry out the following tests of hypothesis:
(a) ${\displaystyle H_0:p=\frac{1}{2}versus{H}_1:p>\frac{1}{2}at\le vel\alpha =.1}$.
(b) ${\displaystyle H_0:p=\frac{1}{2}versus{H}_1:p\ne \frac{1}{2}at\le vel\alpha =.1}$.

Five hundred people were chosen at random from a large population and each was asked whether he or she favoured capital punishment for murderers of police officers. Suppose that 60% of those interviewed said that they were in favour. Let ${\displaystyle \theta }$ denote the proportion of the population who are in favour. Construct a 95% confidence interval for${\displaystyle \theta }$ from the observed data.

Use linear regression to find the equation for the linear function that best fits this data. Click Read Button For online regression calculator. Round both numbers to two decimal places. Write your final answer in a form of an equation ${\displaystyle y=mx+by=mx+b}$
$$\begin{array}{|ccccccc|}\hline x& 1& 2& 3& 4& 5& 6\\ y& 74& 90& 109& 123& 143& 155\\ \hline\end{array}$$

From a classroom of 23 students, the number of students taking Data Management is 13, the number taking Calculus is 9. There are 5 students who are not taking either course.
How many students are taking just Data Management?

Uniform distribution is defined over the interval from 2 to 5.
Show that the total area is 1.00.

Uniform distribution is defined over the interval from 2 to 5.
What is the mean of this uniform distribution?

A study tested the claim that heights of Americans and heights of Austrians have different variances with ${\displaystyle s=7.48092}$ cm for Americans and 7.14756 cm for Austrians. The sample sizes are ${\displaystyle n1=145\text{and}n2=157}$. When using the F test with these data, is it correct to reason that there is no need to check for normalcy because n1 is greater than 30, and n2 is greater than 30?

The amount of chlorine in 100 cm3 water taken from a water tank was measured, the average was 2.15 mg was found. The expert claims that the amount of chlorine in the water is greater than that measured. For this reason, 100 households were randomly selected, with an average chlorine content of 2.55mg and a variance of 0.49 mg. According to this data, find the account value z.

Consider the following data set.
The annual wages of employees at a small accounting firm are given in thousands of dollars.
25 25 30 30 35 35 50 60 16 14 18 18 20
Prepare a frequency distribution for the data set.
$$\begin{array}{|cc|}\hline Wages& Frequency\\ 14\\ 16\\ 18\\ 20\\ 25\\ 30\\ 35\\ 50\\ 60\\ \hline\end{array}$$

An insurance policy sells for $1,000. Based on your past data, an average of 1 in 50 policyholders will file a $9,000 claim, an average of 1 in 100 policyholders will file a $24,000 claim, and an average of 1 in 250 policyholders will file a $55,000 claim. Find the expected value for the company per policy sold.

The following are prices of a sanitizer sold at a few selected stores in a District A during the COVID-19 pandemic. Based on the sample data, at 0.05 level of significance, can we conclude the average price of the sanitizer in District A is RM10.50? Make your conclusion using the p-value approach, with the aid of Mic. Office EXCEL.
RM10.00,RM11.50,RM9.70,RM11.20,RM10.70,RM10.20,RM9.70

An unbalanced coin is weighted so that the probability of heads is 0.55. The coin is tossed ten times.
(a) What is the probability of getting exactly 6 heads?
(b) What is the probability of getting fewer than 3 heads?

A learning management system allows users to take up to 4 different practice exams before taking the actual exam. Data is collected from 40 users of the product regarding the number of practice exams each used.
$$\begin{array}{|cccccc|}\hline \text{Number of Practice Exams Taken}& 0& 1& 2& 3& 4\\ Frequency& 5& 10& 13& 9& 3\\ \hline\end{array}$$
Based on the data, find the estimated probability (relative frequency) that a user will take more than one practice exam.
Given your answer as a decimal.
The probability is ?

The customers at a deli shop can order the lunch special of a sandwich consisting of a meat and a cheese. The meat must be one of these, ham, turkey, bologna, roast beef, or salami. The cheese must be one of these: American, cheddar, provolone, or Swiss. No sandwich compilation is repeated.
According to the given data, how many of the possible sandwich combinations include turkey and American cheese?
A) 20
B) 2
C) 9
D) 1

The following are the annual incomes (in thousands of dollars) for 9 randomly chosen, U.S. adults employed full-time:
68,68,44,82,63,75,51,90,68
(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode: ?
two modes: ? and ?

A group of data has a mean of 65 with a standard deviation of 5. What z-score is possible if the data point is measured at 61 and what is the probability of finding data below the value of 61?

The data below list the number of laptop computers owned by families in each of 40 homes in a subdivision. Draw the frequency distribution of the following list of data. Then find their mean, median and mode. Show your solution.
$$\begin{array}{|cccccccc|}\hline 2& 0& 3& 1& 2& 1& 0& 4\\ 2& 1& 1& 7& 2& 0& 1& 1\\ 0& 2& 2& 1& 3& 2& 2& 1\\ 1& 4& 2& 5& 2& 3& 1& 2\\ 2& 1& 2& 1& 5& 0& 2& 5\\ \hline\end{array}$$

The expected Fisher information
Select one:
a. depends uniquely on data.
b. depends uniquely on the parameter
c. depends uniquely on the sample size n
d. depends on both data and the parameter