?A distribution of exam scores has a mean of \(\mu = 78\). (a) If your score is X = 70

What information is provided by the sign (+/?) of a z-score? What information is provided by the numerical value of the z-score?

A distribution has a standard deviation of \(\sigma=10\). Find the z-score for each of the following locations in the distribution. (a) Above the mean by 5 points. (b) Above the mean by 2 points. (c) Below the mean by 20 points. (d) Below the mean by 15 points. Text Transcription: sigma=10

For a distribution with a standard deviation of \(\sigma=20\), describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z = +1.00 is a location that is 20 points above the mean. (a) z = +2.00 (b) z = +0.50 (c) z = ?1.00 (d) z = ?0.25 Text Transcription: sigma=20

For a population with \(\mu=60\) and \(\sigma=12\), (a) Find the z-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 75 X = 48 X = 84 X = 54 X = 78 X = 51 (b) Find the score (X value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations.) z = 1.00 z = 0.25 z = 1.50 z = ?0.50 z = ?1.25 z = ?2.50 Text Transcription: mu=60 sigma=12

For a population with \(\mu=40\) and \(\sigma=11\), find the z-score for each of the following X values. (Note: You probably will need to use a formula and a calculator to find these values.) X = 45 X = 52 X = 41 X = 30 X = 25 X = 38 Text Transcription: mu=40 sigma=11

For a population with a mean of \(\mu=100\) and a standard deviation of \(\sigma=20\), (a) Find the z-score for each of the following X values. X = 108 X = 115 X = 130 X = 90 X = 88 X = 95 (b) Find the score (X value) that corresponds to each of the following z-scores. z = ?0.40 z = ?0.50 z = 1.80 z = 0.75 z = 1.50 z = ?1.25 Text Transcription: mu=100 sigma=20

A population has a mean of \(\mu=60\) and a standard deviation of \(\sigma=12\). (a) For this population, find the z-score for each of the following X values. X = 69 X = 84 X = 63 X = 54 X = 48 X = 45 (b) For the same population, find the score (X value) that corresponds to each of the following z-scores. z = 0.50 z = 1.50 z = ?2.50 z = ?0.25 z = ?0.50 z = 1.25 Text Transcription: mu=60 sigma=12

Find the z-score corresponding to a score of X = 45 for each of the following distributions. (a) \(\mu=40\) and \(\sigma=20\) (b) \(\mu=40\) and \(\sigma=10\) (c) \(\mu=40\) and \(\sigma=5\) (d) \(\mu=40\) and \(\sigma=2\) Text Transcription: mu=40 sigma=20 sigma=10 sigma=5 sigma=2

Find the X value corresponding to z = 0.25 for each of the following distributions. (a) \(\mu=40\) and \(\sigma=4\) (b) \(\mu=40\) and \(\sigma=8\) (c) \(\mu=40\) and \(\sigma=16\) (d) \(\mu=40\) and \(\sigma=32\) Text Transcription: mu=40 sigma=4 sigma=8 sigma=16 sigma=32

A score that is 6 points below the mean corresponds to a z-score of z = ?2.00. What is the population standard deviation?

A score that is 9 points above the mean corresponds to a z-score of z = 1.50. What is the population standard deviation?

For a population with a standard deviation of \(\sigma=12\), a score of X = 44 corresponds to z = ?0.50. What is the population mean? Text Transcription: sigma=12

For a population with a mean of \(\mu=70\), a score of X = 64 corresponds to z = ?1.50. What is the population standard deviation? Text Transcription: mu=70

In a population distribution, a score of X = 28 corresponds to z = ?1.00 and a score of X = 34 corresponds to z = ?0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.)

For each of the following populations, would a score of X = 85 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? (a) \(\mu=75\) and \(\sigma=15\) (b) \(\mu=80\) and \(\sigma=2\) (c) \(\mu=90\) and \(\sigma=20\) (d) \(\mu=93\) and \(\sigma=3\) Text Transcription: mu=75 sigma=15 mu=80 sigma=2 mu=90 sigma=20 mu=93 sigma=3

A distribution of exam scores has a mean of \(\mu = 78\). (a) If your score is X = 70, which standard deviation would give you a better grade: \(\sigma = 4\) or \(\sigma = 8\)? (b) If your score is X = 80, which standard deviation would give you a better grade: \(\sigma = 4\) or \(\sigma = 8\)? Text Transcription: mu = 78 sigma = 4 sigma = 8

For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. (a) A score of X=70, on an exam with M=82 and \(\sigma=8\); or a score of X=60 on an exam with \(\mu=72\) and \(\sigma=12\). (b) A score of X=58, on an exam with \(\mu=49\) and \(\sigma=6\); or a score of X=85 on an exam with \(\mu=70\) and \(\sigma=10\). (c) A score of X=32, on an exam with \(\mu=24\) and \(\sigma=4\); or a score of X=26 on an exam with \(\mu=20\) and \(\sigma=2\). Text Transcription: sigma=8 mu=72 sigma=12 mu=49 sigma=6 mu=70 sigma=10 mu=24 sigma=4 mu=20 sigma=2

A distribution with a mean of \(\mu=38\) and a standard deviation of \(\sigma=5\) is transformed into a standardized distribution with \(\mu=50\) and \(\sigma=10\). Find the new, standardized score for each of the following values from the original population. (a) X = 39 (b) X = 43 (c) X = 35 (d) X = 28 Text Transcription: mu=38 sigma=5 mu=50 sigma=10

A distribution with a mean of \(\mu=76\) and a standard deviation of \(\sigma=12\) is transformed into a standardized distribution with \(\mu=100\) and \(\sigma=20\). Find the new, standardized score for each of the following values from the original population. (a) X = 61 (b) X = 70 (c) X = 85 (d) X = 94 Text Transcription: mu=76 sigma=12 mu=100 sigma=20

A population consists of the following N = 5 scores: 0, 6, 4, 3, and 12. (a) Compute \(\mu\) and \(\sigma\) for the population. (b) Find the z-score for each score in the population. (c) Transform the original population into a new population of N = 5 scores with a mean of \(\mu = 100\) and a standard deviation of \(\sigma = 20\). Text Transcription: mu sigma mu=100 sigma=20

A sample has a mean of M = 30 and a standard deviation of s = 8. Find the z-score for each of the following X values from this sample. X = 32 X = 34 X = 36 X = 28 X = 20 X = 18

A sample has a mean of M = 25 and a standard deviation of s = 5. For this sample, find the X value corresponding to each of the following z-scores. z = 0.40 z = 1.20 z = 2.00 z = ?0.80 z = ?0.60 z = ?1.40

For a sample with a standard deviation of s = 8, a score of X = 65 corresponds to z = 1.50. What is the sample mean?

For a sample with a mean of M = 51, a score of X = 59 corresponds to z = 2.00. What is the sample standard deviation?

In a sample distribution, X = 56 corresponds to z = 1.00, and X = 47 corresponds to z = ?0.50. Find the mean and standard deviation for the sample.

A sample consists of the following n = 7 scores: 5, 0, 4, 5, 1, 2, and 4. (a) Compute the mean and standard deviation for the sample. (b) Find the z-score for each score in the sample. (c) Transform the original sample into a new sample with a mean of M = 50 and s = 10.