Find the z-score location of a vertical line that separates a normal distribution as described in each of the following.  5% in the tail on the left 30% in the tail on the right 65% in the body on the left 80% in the body on the right 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   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.   IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ =15. Find the proportion of the population in each of the following IQ categories. Genius or near genius: IQ over 140 Very superior intelligence: IQ from 120–140 Average or normal intelligence: IQ from 90–109   A true/false test has 20 questions. If a student is simply guessing at the answers, On average, how many questions would a student answer correctly for the entire test? What is the probability that a student would answer more than 15 questions correctly simply by guessing? What is the probability that a student would answer fewer than 7 questions correctly simply by guessing? A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing. What is the probability of correctly predicting exactly 20 cards in a series of 100 trials? What is the probability of correctly predicting 10 or more cards in a series of 36 trials? What is the probability of correctly predicting more than 16 cards in a series of 64 trials?

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Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. 

  1. 5% in the tail on the left
  2. 30% in the tail on the right
  3. 65% in the body on the left
  4. 80% in the body on the right
  5. 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.
  6. X = 72
  7. X = 76
  8. X = 66
  9. X = 60

 

  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. IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ =15. Find the proportion of the population in each of the following IQ categories.
  2. Genius or near genius: IQ over 140
  3. Very superior intelligence: IQ from 120–140
  4. Average or normal intelligence: IQ from 90–109

 

  1. A true/false test has 20 questions. If a student is simply guessing at the answers,
  2. On average, how many questions would a student answer correctly for the entire test?
  3. What is the probability that a student would answer more than 15 questions correctly simply by guessing?
  4. What is the probability that a student would answer fewer than 7 questions correctly simply by guessing?
  5. A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing.
  6. What is the probability of correctly predicting exactly 20 cards in a series of 100 trials?
  7. What is the probability of correctly predicting 10 or more cards in a series of 36 trials?
  8. What is the probability of correctly predicting more than 16 cards in a series of 64 trials?

 

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