Sampling Distribution Examples with Solutions

Recent questions in Sampling distributions

A population of values has a normal distribution with $μ = 121.3$ and $σ = 5.8$ . You intend to draw a random sample of size $n = 149$ .
Find the probability that a single randomly selected value is between 119.8 and 121.2.
P(119.8 < X < 121.2)
Find the probability that a sample of size $n = 149$ is randomly selected with a mean between 119.8 and 121.2.
P(119.8 < M < 121.2)
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

İrem YADEL2022-04-02

(a) Evaluate the standard deviation s for each set of data.
(b) Pool the data to obtain an absolute standard deviation
for the method.

Brämhults Juice, based in Sweden, produces chilled fruit and vegetable juices. A manager at Brämhults is considering purchasing a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of 100% pure carrot juice and wants an estimate of the differ- ence in the mean filling weights between the new machine and the old machine. Random samples of bottles of carrot juice that had been filled by both machines were obtained. Estimate the difference in the mean filling weights between the new and the old machines? Discuss the assumptions. Use a = 0.10.

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 336 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county.

A strawberry jam company regularly receives large shipments of strawberries. For each shipment that is received, a supervisor takes a random sample of 500 strawberries to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10%, percent of the entire shipment of strawberries is bruised, then they will request a new shipment of strawberries.

Let p represent the proportion of the strawberries in a shipment that are bruised.

ringbarsh1i 2022-02-12

Which of the following is true about the sampling distribution of means?
Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.
Shape of the sampling distribution of means is always the same shape as the population distribution, no matter what the sample size is.
Sampling distributions of means get closer to normality as the sample size increases.
Sampling distributions of means are always nearly normal.

the row of numbers shown below to generate 12 random numbers between 01 and 99 09075 11123 14740 39704 88198 93469 52264 39270

socorraob 2022-01-05

The resuts of a recent statewide test suggested that the proportion is 0.74. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?
A sample of 7410 elementary school children is needed to obtain a 99.9% confidence interval with a margin of error of 0.07.

Problem 1: A machine is producing metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 cm. Find a 99% confidence interval of the true mean diameter of pieces from this machine, assuming an approximate normal distribution.

Zoe Oneal 2021-10-26

Which of the following statistics are unbiased estimators of population parameters?
Choose the correct answer below. Select all that apply.
A) Choose the correct answer below. Select all that apply.
B) Sample variance used to estimate a population variance.
C) Sample proportion used to estimate a population proportion.
D) Sample mean used to estimate a population mean.
E) Sample range used to estimate a population range.
F) Sample standard deviation used to estimate a population standard deviation

Nann 2021-08-14

Resource managers of forest game lands were concerned about the size of the deer and rabbit populations during the winter months in a particular forest. As an estimate of population size, they proposed using the average number of pellet groups for rabbits and deer per 30-foot-square plots. From an aerial photograph, the forest was divided into N= 10,000 30-foot-square grids. A simple random sample of 2 = 500 plots was taken, and the number of pellet groups was observed for rabbits and for deer. The results of this study are summarized in the accompanying table.
a. Estimate $μ_{1}, and μ_{2}$ , the average number of pellet groups for deer and rabbits, respectively, per 30-foot-square-plots. Place bounds on the errors of estimation.
b. Estimate the difference in the mean size of pellet groups per plot for the two animals, with an appropriate margin of error.
Deer
Sample mean = 2.30
Sample variance = 0.65
Rabbits
Sample mean = 4.52
Sample variance = 0.97

Isa Trevino 2021-06-26

Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article ''Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis'' (Intl. J. of Advanced Manuf. Tech., 2010: 117–134)). If $\bar{X}$ is the sample mean Young’s modulus for a random sample of $n = 16$ sheets, where is the sampling distribution of $\bar{X}$ centered, and what is the standard deviation of the $\bar{X}$ distribution?

ossidianaZ 2021-06-13

Describe how to use random numbers to simulate the following PERFORMANCES:
(a) A basketball player has the ABILITY to make 40% of his shots and he takes 25 shots in a game.
(b) A basketball player has the ABILITY to make 75.2% of her free-throws and she takes 8 free throws in a game.

FizeauV 2021-06-04

Consider the two samples of data from the McKenzie School. The numbers represent the time in seconds that it took each child to cover a distance of 50 meters. Girls’ Times: 8.3, 8.6, 9.5, 9.5, 9.6, 9.8, 9.9, 9.9, 10.0, 10.0, 10.0, 10.1, 10.3, 10.5 Boys’ Times: 7.9, 8.0, 8.2, 8.2, 8.4, 8.6, 8.8, 9.1, 9.3, 9.5, 9.8, 9.8, 10.0, 10.1, 10.3. Based on the sample means, do you conclude that the distributions of times from the boys’ population and girls’ population are different? Explain.

aflacatn 2021-05-28

Represent sampling distributions in the format of a table that lists the different values of the sample statistic along with their corresponding probabilities. Given that the data consist of ranks, does it really make sense to identify the sampling distribution of the sample means?

Falak Kinney 2021-05-27

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
$H_{0} : P = 0.52$ versus $H_{1} : p < 0.52$
$N = 150, X = 72, α = 0.1$
Is $N P_{0} (1 - P_{0})$ greater than or equal to 10?
Use technology to find the P-Value.

Brennan Flores 2021-05-21

When comparing two sets of data values, what is the advantage of using relative frequency distributions instead of frequency distributions?

Carol Gates 2021-05-19

Use the row of numbers shown below to generate 12 random numbers between 01 and 99.
78038 18022 84755 23146 12720 70910 49732 79606
Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?

e1s2kat26 2021-05-18

Solve by using the strategy Work Backward. A beetle needs to climb out of a crater that is 800 cm deep. It advances 120 cm each day, but is slips back 90 cm while resting each night. How many days will it take before this beetle successfully climbs out of the crater?

Reeves 2021-05-16

Carol and Alina play soccer for a local college team. Based on anecdotal evidence, they think that there is a difference in a player success rate of taking penalty kicks with their dominant foot compared to their non-dominant foot. They would like to test this hypothesis with an experiment. Carol arranges for each of the 11 starting players on her team to take ten penalty kicks with their dominant foot and ten penalty kicks with their non dominant foot and records the data. Using the same data values, describe two distributions that would be more supportive of the hypothesis.

In simple terms, this mathematical branch will be familiar to students dealing with probability distribution and statistics as you seek answers to your random sample statistic equations. Take a look at the sampling distribution example that will make things clearer regardless of your subject. If you need additional help, consider sampling distribution examples with solutions that will have all the questions that will look alike to what you may have with your statistics regardless if there are sampling distribution problems or a complex sampling distribution equation. As always, start with sampling distribution questions first to identify the most efficient solution.

Understanding Sampling Distribution with Plainmath