Z-score & Probability
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1. A distribution has a standard deviation of o = 8. Find the z-score for each of the following locations in the distribution.
a. Above the mean by 4 points.
b. Above the mean by 16 points
c. Below the mean by 8 points
d. Below the mean by 12 points
2. For a population with u = 100 and a standard deviation of o = 10,
a. Find the z-score for each of the following X values.
X = 105 X = 120 X= 130
X= 90 X = 85 X = 60
b. Find the score (X value) that corresponds to each of the following z-scores.
Z = -1.00 z = -0.50 z = 2.00
Z = 0.70 z = 1.50 z= -1.50
3. Find the z-score corresponding to a score of X= 60 for each of the following distributions.
a. u = 50 and o = 10
b. u = 50 and o = 5
c. u=70 and o = 20
d. u = 70 and o = 5
4. For a population with a standard deviation of o = 10, a score of X= 44 corresponds to z = -0.50. What is the population mean?
5. A kindergarten class consists of 14 boys and 11 girls. If the teacher selects children from the class using random sampling,
a. What is the probability that the first child selected will be a girl?
b. If the teacher selects a random sample of n = 3 children and the first two children are both boys, what is the probability that the third child selected will be a girl?
6. For each of the following z- scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then, determine whether the body is to the right or the left of the line and find the proportion in the body.
a. z= 1.00 b. z= -0.50
c. z= 1.50 d. z = -2.00
7. For a normal distribution, identify the z-score location that would separate the distribution into two sections so that there is
a. 70% in the body on the right-hand side.
b. 80% in the body on the right hand side.
c. 75% in the body on the left hand side.
d. 90% in the body on the left hand side.
8. A normal distribution has u = 80 and o = 20. For each of the following scores, indicate whether the tail of the distribution is located to the right or the left of the score, and find the proportion of the distribution located in the tail.
a. X= 85 b. X= 92
c. X = 70 D. X = 64 hide problem
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Solution Summary
The solution provides step by step method for the calculation of Z score and probability. Formula for the calculation and Interpretations of the results are also included.
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