A colony of laboratory rats contains 18 white rats and 7 spotted rats. What is the probability of randomly selecting a white rat from this colony?A jar contains 20 red marbles and 10 blue marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both red, what is the probability that the third marble also will be red?A normal distribution has a mean of μ = 70 and a standard deviation of σ = 8. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail.X = 72X = 76X = 66X = 60According to a recent report, people smile an average of μ = 62 time per day. Assuming that the distribution of smiles is approximately normal with a standard deviation of σ = 18, find each of the following values.What proportion of people smile more than 80 times a day?What proportion of people smile at least 50 times a day? For a normal distribution with a mean of μ = 60 and a standard deviation of σ = 10, find the proportion of the population corresponding to each of the following.Scores greater than 65.Scores less than 68.Scores between 50 and 70. A normal distribution has a mean of μ = 30 and a standard deviation of σ = 12. For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body.X = 33X = 18X = 24X = 39 Find each of the following probabilities for a normal distribution.p(z > 1.25)p(z > –0.60)p(z < 0.70)p(z < –1.30) A normal population has µ = 50 and σ = 8. A random sample of n = 16 scores from this population has a mean of 54. What is the z-score for this sample mean? A random sample of n = 9 scores is obtained from a population with µ = 50 and σ = 9. If the sample mean is M = 53, what is the z-score corresponding to the sample mean? A random sample of n = 25 scores is selected from a normally distributed population with μ = 500 and σ = 100. What is the probability that the sample mean will be less than 490? For samples selected from a population with µ = 100 and σ = 15, which of the following has the smallest standard error?a sample of n = 4 scoresa sample of n = 16 scoresa sample of n = 25 scoresThe three samples all have the same standard error For a population with a mean of μ = 45 and a standard deviation of σ = 10, what is the standard error of the distribution of sample means for each of the following sample sizes?n = 4 scoresn = 25 scores A population forms a normal distribution with a mean of μ = 55 and a standard deviation of σ = 12. For each of the following samples, compute the z-score for the sample mean.M = 58 for n = 4 scoresM = 58 for n = 16 scoresM = 58 for n = 36 scores 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 μ = 60 and σ = 10.If it was obtained from a population with μ = 60 and σ = 20.If it was obtained from a population with μ = 60 and σ = 40

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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A colony of laboratory rats contains 18 white rats and 7 spotted rats. What is the probability of randomly selecting a white rat from this colony?
A jar contains 20 red marbles and 10 blue marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both red, what is the probability that the third marble also will be red?
A normal distribution has a mean of μ = 70 and a standard deviation of σ = 8. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail.

X = 72
X = 76
X = 66
X = 60
According to a recent report, people smile an average of μ = 62 time per day. Assuming that the distribution of smiles is approximately normal with a standard deviation of σ = 18, find each of the following values.
What proportion of people smile more than 80 times a day?
What proportion of people smile at least 50 times a day?

For a normal distribution with a mean of μ = 60 and a standard deviation of σ = 10, find the proportion of the population corresponding to each of the following.
Scores greater than 65.
Scores less than 68.
Scores between 50 and 70.

A normal distribution has a mean of μ = 30 and a standard deviation of σ = 12. For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body.
X = 33
X = 18
X = 24
X = 39

Find each of the following probabilities for a normal distribution.
p(z > 1.25)
p(z > –0.60)
p(z < 0.70)
p(z < –1.30)

A normal population has µ = 50 and σ = 8. A random sample of n = 16 scores from this population has a mean of 54. What is the z-score for this sample mean?

A random sample of n = 9 scores is obtained from a population with µ = 50 and σ = 9. If the sample mean is M = 53, what is the z-score corresponding to the sample mean?

A random sample of n = 25 scores is selected from a normally distributed population with μ = 500 and σ = 100. What is the probability that the sample mean will be less than 490?

For samples selected from a population with µ = 100 and σ = 15, which of the following has the smallest standard error?
a sample of n = 4 scores
a sample of n = 16 scores
a sample of n = 25 scores
The three samples all have the same standard error

For a population with a mean of μ = 45 and a standard deviation of σ = 10, what is the standard error of the distribution of sample means for each of the following sample sizes?
n = 4 scores
n = 25 scores

A population forms a normal distribution with a mean of μ = 55 and a standard deviation of σ = 12. For each of the following samples, compute the z-score for the sample mean.
M = 58 for n = 4 scores
M = 58 for n = 16 scores
M = 58 for n = 36 scores

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 μ = 60 and σ = 10.
If it was obtained from a population with μ = 60 and σ = 20.
If it was obtained from a population with μ = 60 and σ = 40

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