Data Distribution Questions and Answers

Suppose you are reviewing your cell phone bill on Friday and you notice you go over your data limit 49% of the time. You review the weather forecast for tomorrow that says there is a 11% chance of rain. Assuming rain and going over in data are independent events, what is the probability that it rains and you go over in data tomorrow? Give your answer as an exact fraction and reduce the fraction as much as possible

A newspaper article reported that 400 people in one state were surveyed and 70% were opposed to a recent court decision. The same article reported that a similar survey of 500 people in another state indicated opposition by only 40%. Construct a 95% confidence interval of the difference in population proportions based on the data.

The following data set was collected by Campus Life. They are investigating the possibility of a relationship between students' satisfaction with Penn State (on a scale of 1-10 where higher numbers indicate greater satisfaction) and how many activities they participate in on campus. In this table, each "ID" represents a single student.
1. Imagine that someone in campus life wants to convert the "Satisfaction" scale of 1-10 to a scale of 1-100. 2. Would the covariance get larger, smaller, or stay the same?
3. Would the correlation coefficient r become larger, smaller, or stay the same?
4. What would be an example of an impossible correlation coefficient? In other words, give a value of r that would lead you to suspect that the researcher made a mistake.
5. Imagine a study where all our data (x, y) falls perfectly on a flat and straight horizontal line. If we calculated the correlation coefficient r for this data, what would it be? What would that mean for our hypotheses?
$$\begin{array}{|ccc|}\hline StudentID& Satisfaction& Activities\\ 1& 7& 10\\ 2& 6& 4\\ 3& 2& 0\\ 4& 4& 13\\ 5& 1& 7\\ 6& 7& 15\\ 7& 6& 10\\ 8& 6& 12\\ 9& 3& 8\\ 10& 8& 21\\ Mean& 5.0& 10.0\\ Std.Dev& 2.4& 5.9\\ \hline\end{array}$$

HBL Bank Pvt LtD. is studying its ATM use in the Gulshan-e-Iqbal area of Karachi. A sample of 30 ATMs showed they were used in the given number of times (in seconds) on a particular day, as shown in Table 1.
Identify the presence of outliers in this dataset After removing the outliers (if present) from the given dataset, what is the expected or average number of times (in seconds) the ATM is used in the new dataset (if outliers were detected and removed). Show your results with errors in the statistical expected or average value.
$$\overline{)\begin{array}{cccccccccc}83.24& 64.01& 84.23& 76.20& 84.21& 54.29& 5.11& 59.21& 70.23& 61.01\\ 63.10& 80.23& 84.21& 73.20& 68.11& 52.19& 65.22& 90.16& 52.16& 177.21\\ 95.23& 36.15& 48.12& 16.18& 59.32& 84.22& 195.13& 47.18& 87.13& 26.11\end{array}}$$

Find the range and standard deviation of the set of data.
5,8,5,8,8,10,12
The range is 7.
The standard deviation is ?

You measure the length of copperheads in cm. You want to know if there is a difference in length between male and female copperheads. You get the following results, but discover the data are NOT normally distributed.
$$\begin{array}{|c|}\hline Sex\\ males:& 64& 72& 73& 74& 76& 76& 77& 114& 78.25& 15.01\\ females:& 31& 54& 55& 56& 57& 58& 65& 67& 55.38& 10.91\\ \hline\end{array}$$
Give the value of the test statistic (e.g., U* or t*, whichever is correct) for these data.

Last week a gumball machine dispensed 10 white gumballs and 16 other gumballs. Considering this data, how many of the next 78 gumballs dispensed should you expect to be white gumballs?

About 4% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000. (Remember that means should be rounded to one more decimal place than the raw data.)

In the table, the class median values ​​for the classified data are given as mi and the frequencies as fi Calculate the coefficient of variation for the data set.
$$\begin{array}{|cccc|}\hline m_i& f_i& m_i{f}_i& m_i^2{f}_i\\ 5& 5& 25& 125\\ 10& 12& 120& 1200\\ 15& 10& 150& 2250\\ 20& 3& 60& 1200\\ & 30& 355& 4775\\ \hline\end{array}$$

Find the slope of the regression line for the following data.
$$\begin{array}{|cc|}\hline x& y\\ 1& 1\\ 3& 2\\ 3& 1\\ \hline\end{array}$$
We have written the regression line in the form ${\displaystyle y=b_0+b_{1}x}$. So in this problem you only need to find the value of ${\displaystyle b_1}$.

Complete the given table below by writing directly the needed data. Show complete solution in solving the Mean, Variance and Standard Deviation.
$$\begin{array}{|cccccc|}\hline x& P(x)& x\cdot P(x)& x-\mu & (x-\mu {)}^2& (x-\mu {)}^{2}P(x)\\ 0& 0.11\\ 1& 0.22\\ 2& 0.33\\ 3& 0.25\\ 4& 0.09\\ \hline\end{array}$$

Consider the data: 12, 9, 11, 15, 13, 15, 16. (Show your work.)
d) Determine the mode
e) Determine the range.

Assume that we have observations from two different populations. The data collected have sample sizes ${\displaystyle n_1=25\text{and}{n}_2=29}$. The mean of sample 1 is 18 and the mean of sample 2 is 16. Furthermore, the sample standard deviations are ${\displaystyle s_1=5}$ and ${\displaystyle s_2=6}$. For these data, the estimated standard error of the difference of the two means is:
A. 11 B. 0.4 C. 1.5 D. 61 E. none of the preceding

The following data recorded the time it took for a sample of seven different species of frogsand

If the distribution of hate crimes was normally distributed, we would expect 68 percent of the data points to be within 1 standard deviations of the mean?
1) What percent of your 12 data points fall within ${\displaystyle \mu -\sigma \to \mu +\sigma }$ (In other words 1 SD on both sides of your mean)? You will need to count how many of the 12 data points fall within these two values, then divide by 12.
Give answer as a percent.
2) Get ${\displaystyle u-2\sigma }$ (The mean -2' the standard deviation: Two SD below the mean)3) Get ${\displaystyle \mu +2\sigma }$ (the mean +2' the standard deviation: Two SD above the mean)
If the distribution of hate crimes was normally distributed, we would expect 95 percent of the data points to be within 2 standard deviations of the mean?
4) What percent of your 12 data points fall within ${\displaystyle \mu -2\sigma \to \mu +2\sigma }$ (In other words 2 SD on both sides of your mean)?
Give answer as a percent.

Find the percentile for the data value 29.
Data: 9 10 10 11 13 14 16 17 17 18 19 20 22 23 25 27 28 29 30 32 33 34 36 37 39 40 41 42 44 46 49 50 53 55 56

What is the mean of the following data:
0,0,1,1,1,2,2,2,3,3

Calculate least squares estimates of the slope and intercept to the following data:
$$\begin{array}{|ccccccc|}\hline x& 2& 7& 9& 1& 5& 12\\ y& 13& 21& 23& 14& 15& 21\\ \hline\end{array}$$

Let us now assume that the length of one year of artic char follows normal distributions with an average of 127 cm and a standard deviation of 16 cm.
a) If an artic char is chosen at random, what is the probability that it is longer than 140 cm?
b) Should the arctic char be in the group of the 5% longest arctic char when itis one year old, how big does it have to be?