Data Distribution Questions and Answers

On average, a J&T delivery rider can deliver 10 packages to their respective owners in one hour. Based on this data, what is the probability that the rider can deliver at most 4 packages in half an hour? Use Poisson distribution.
a. 0.9329
b. 0.7185
c. 0.2331
d. 0.6715
e. 0.2851
f. 0.4405
g. 0.5595
h. 0.6751

Porosity measurements in several oil fields show a normal distribution with a mean of 5% and a standard deviation of 1%. A total of 25 measurements are collected randomly from the available data. Determine the minimum value of the mean of porosity for such a sample so that the probability to have it lower than it is 5%.
Select one:
a. 4.67
b. 3.36
c. 4.75
d. 4.61

Rock noise in an underground mine occurs at an average rate of three per hour. Find the probability that no rock noise will be recorded for at least 30 minutes.

A die is loaded in a such a way that probabilities of getting 1, 2, 3, 4, 5, 6 are 1/2, 1/6, 1/12, 1/12, 1/12 and 1/12.
a. Construct the probability distribution for the data.
b. Find the mean and the variance of the probability distribution.

A wallet containing four P100 bills, two P200 bills, three P500 bills, and one P1,000 bill. Construct a probability distribution table for the data.

The chart below represents the number of juices sold in the cafeteria before school one mornung.
$$\begin{array}{|cc|}\hline \text{Type of Juice}& \text{Number Sold}\\ Apple& 10\\ Orange& 18\\ Grapefruit& 7\\ Cranberry& 3\\ Tomato& 2\\ \hline\end{array}$$
Based on this data, if Marcel bought a juice at random, what is that probability that he bought an orange or graphefruit juice?
A) ${\displaystyle \frac{9}{20}}$
B) ${\displaystyle \frac{7}{18}}$
C) ${\displaystyle \frac{2}{5}}$
D) ${\displaystyle \frac{5}{8}}$

Different students groups in a class of the Department of Chemistry were conducting lab experiments to determine changes in number of moles of chemical-A due to addition of different samples of chemical-B. They got the following results:
9.7,3.4,7.4,3.9,5.2,6.7,3.9,3.3,9.8,2.9,6.2,9.6
Calculate the sample variance value of the data.
Note: The answer must be written using two decimal places.
Answer: ?
Different students groups in a class of the Department of Chemistry were conducting lab experiments to determine changes in number of moles of chemical-A due to addition of different samples of chemical-B. They got the following results:
3.8,2.7,2,3.5,2,10,1.4,4.9,3.5,3.5,1.4,5.3,4.6,6.7,6.8,2.9,3.8,4.6
Calculate the sample range of the data.
Note: The answer must be written using two decimal places.
Answer: ?

Use the following data set: 8, 3, 5, 2, 8, 4, 2, 6, 7, 5, 8 to answer questions The mid-range of the data is………

Use the following data set: 7,17,30,18,24,16,3,18,7 to answer questions
The data is said to be
Select one:
a. bimodal
b. has no mode
c. multimodal
d. Unimodal

The heights of American adult males are normally distributed with a mean of 177 cm and a standard deviation of 7.4 cm. Use the Empirical Rule to find the range of heights that contain approximately
(a) 68% of the data
? cm ? cm
(b) 95% of the data
? cm ?cm
(c) 99.7% of the data
? cm ? cm

Differentiate the three measures of central tendency: ungrouped data.

LightCastle Partners, a Bangladeshi business management consultant, employs a large number of data analysts to analyze the data in a survey project. The time it takes for new data analysts to learn the analysts procedure is known to have a normal distribution with a mean of 82 minutes and a standard deviation of 11 minutes.
a. What is the probability that the new data analysts will take more than 77 minutes to learn the analysis procedure?
b. What is the probability that the new data analysts will take between 54 to 85 minutes to learn the analysis procedure?
c. To maintain employee standars, LightCastle does not hire any analyst who fails to learn the process within a specified time. Therefore, what should be the specified time limit if they wish to retain at most 72.67% of new analysts?
? minutes

LightCastle, a Bangladeshi business management consultant, employs a large number of data analysts to analyze the data in survey project. The time it takes for new data analysts to learn the analysis procedure is known to have a normal distribution with a mean of 101 minutes and a standard.
a. What is the probability that the new data analysts will take more than 123 minutes to learn the analysis procedure?
b. What is the probability that the new data analysts will take between 97 to 141 minutes to learn the analysis procedure?
c. To maintain employee standars, LightCastle does not hire any analyst who fails to learn the process within a specified time. Therefore, what should be the specified time limit if they wish to retain at most 95.59% of new analysts?

Consider the following data set for a population: 26,27,32,29,35,38,30,18,31,34.
This data set has a mean of 30. Given that the z-score represents the distance from the mean in terms of the standatd deviation, the score in the data set that would have the largest z-score in magnitude would be

An advertising campaign for a new product is tergeted to make 20% of the adult population in a metropolitan area aware of the product. After the campaign, a random sample of 400 adults in the metropolitan area is obtained.
i. Find the approximate probability that 57 or fewer adults in the sample are aware of the product.
ii. Should the approximation in part i. be accurate?

A TIRE MANUFACTURER WANTS TO DETERMINE THE INNER DIAMETER OF A CERTAIN GRADE OF TIRE. IDEALLY, THE DIAMETER WOULD BE 570 MM. THE DATA ARE AS FOLLOWS:
572, 572, 573, 568, 569, 575, 565, 570.
(A) FIND THE SAMPLE MEAN AND MEDIAN.
(B) FIND THE SAMPLE VARIANCE, STANDARD DEVIATION, AND RANGE.

Using the coefficient of variation, how much (%) do these data sets vary?
(rounding to the nearest percent)
Data Set 1: ${\displaystyle \bar{x}=12\text{and}s=7}$
Data Set 2: ${\displaystyle \bar{x}=0.12\text{and}s=0.3}$

A recent study by the EPA has determined that the amount of contaminants in Minnesota lakes (in parts per million) is normally distributed with mean 64 ppm and variance 17.6. Suppose 35 lakes are randomly selected and sampled. What is the probability that the sample average amount of contaminants is (a) Above 72 ppm? (b) Between 64 and 72 ppm? (c) Exactly 64 ppm.