A group of scientists is measuring an unknown quantity μER by repeatingindependent experiments. Let X be the value measured by the k-th experiment. Ifthe experiment is repeated for n times, the approximated value of μ, is given by thesample meanXn=X₁ + ... + XnN(The actual quantity is the (common) expected value of Xk.) They have a strongevidence that each X has an approximated standard deviation o= 3. Use centrallimit theorem to estimate how many experiments to repeat in order to be 98% surethat the approximated mean Xn is within 0.1 margin of error from the actual valuefe?

Given, Standard deviation is 3, confidence interval is 98% and margin of error is 0.1.

Answered: (c) A group of scientists is measuring…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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18
If the random variable of X is normally distributed with a mean of 50 and a standard deviation of 10, approximately what % of all possible observed values of X will lie between 30 and 70.
A persons blood glucose level and diabetes are closely related XB a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Supposed to after a 12 hour fast the random variable X will have a distribution that is approximately normal with mean of u=87 and a standard deviation of O=25. Note: after 50 years of age both the mean and Standard deviation tends to increase for an adult under 50 after 12 hour fast find the following probabilities A) X is more than 60 B) X is less than 60 C) X is between 60 and 110 D) X is greater than 125 (borderline diabetes starts at 125)
The next six questions refer to the following scenario: A random sample of 25 students were asked to self-identify as "statistics-lovers" or "statistics-adorers." 16 students self-identified as "lovers" and 9 students as "adorers." Below table summarizes the mean of a statistics test and standard deviation that was given after the self-identification. Test the following hypothesis at alpha=5% (0.05). HO: Mean Statistics Lovers = Mean Statistics Adorers HA: Mean Statistics Lovers Mean Statistics Adorers You can assume equal variance.
If the z-value for a given x of a random variable Z is z =1.06, and the distribution of X is normal with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?
25. Each of a random sample of 30 student nurses who participated in a research project was given a test designed to measure the degree of creative thinking. The standard deviation of the scores was 11. Can one conclude from these data that the population variance is less than 400? Let α = 0. 05 and assume that the population is normally distributed. (A) Yes (B) No
A sample of n=25 scores has a mean of M=68. Find the z-score for this sample: If it was obtained from a population with m=60 and s=10. If it was obtained from a population with m=60 and s=20. If it was obtained from a population with m=60 and s=40. A normal distribution has a mean of μ = 54 and a standard deviation of σ = 6. What is the probability of randomly selecting a score less than X = 51? What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51? What is the probability of selecting a sample of n = 36 scores with a mean less than M = 51? A sample is selected from a population with a mean of and a standard deviation of . If the sample has scores, what is the expected value of and the standard error of If the sample has scores, what is the expected value of and the standard error of ? A random sample is obtained from a normal population with a mean of and a standard deviation of . The sample mean is Is this a…
You have taken a random sample of size n = 12 from a normal population that has a population mean of μ = 90 and a population standard deviation of G = 4. Your sample, which is Sample 1 in the table below, has a mean of x=89.1. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 80% and 95% confidence intervals for the population mean. Use 1.282 for the critical value for the 80% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.) • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. • For the points (and ◆), enter the population mean, μ = 90. 85.0 S1 |+H 85.0 80% confidence interval 91.0 X +|||||||| x 80% 80% 95% 95% lower upper lower upper limit limit limit limit ? 89.1 ? ? ? S2 90.7 89.2 92.2 88.4 93.0 S3 89.8 88.3 91.3 87.5 92.1 S4 91.9 90.4 S5 89.4 87.9 S6 90.8 89.3 S7 90.6…
If all possible samples of size 16 are drawn from a normal population with mean equal to 50 and standard deviation equal to 5, what is the probability that a sample mean, ,will fall in the interval from Hx-1.90g to Hx –0.40g ? Assume that the sample means can be measured to any degree of accuracy.
Solve question #9 for part D only.
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 140 (borderline diabetes starts at 140)

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