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.

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  1. 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?
  2. 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?
  3. 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.
  1. X = 72
  2. X = 76
  3. X = 66
  4. X = 60
  5. 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.
  6. What proportion of people smile more than 80 times a day?
  7. What proportion of people smile at least 50 times a day?

 

  1. 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.
  2. Scores greater than 65.
  3. Scores less than 68.
  4. Scores between 50 and 70.

 

  1. 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.
  2. X = 33
  3. X = 18
  4. X = 24
  5. X = 39

 

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

 

  1. 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?

 

  1. 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?

 

  1. 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?

 

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

 

  1. 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?
  2. n = 4 scores
  3. n = 25 scores

 

  1. 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.
  2. M = 58 for n = 4 scores
  3. M = 58 for n = 16 scores
  4. M = 58 for n = 36 scores

 

  1. A sample of n = 25 scores has a mean of M = 68. Find the z-score for this sample:
  2. If it was obtained from a population with μ = 60 and σ = 10.
  3. If it was obtained from a population with μ = 60 and σ = 20.
  4. If it was obtained from a population with μ = 60 and σ = 40
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