Sample Question: Normal Probability

See attached file.

1. For a population with a mean of µ=60 and a standard deviation of ?=24, find the z-score corresponding to each of the following samples.
A. M=63 for a sample of n=16 scores
B. M=63 for a sample of n=36 scores
C. M=63 for a sample of n=64 scores

2. A population of scores forms a normal distribution with a mean of µ=40 and a standard deviation of ?=12.
A. What is the probability of randomly selecting a score less than X=34?
B. What is the probability of selecting a sample of n=9 scores with a mean less than M=34?
C. What is the probability of selecting a sample of n=36 scores with a mean less than M=34?

3. The population of SAT scores forms a normal distribution with a mean of µ=500 and a standard deviation of ?=100. If the average SAT score is calculated for a sample of n=25 students,
A. What is the probability that the sample mean will be greater than M=510. In symbols, what is p(M>510)?
B. What is the probability that the sample mean will be greater than M=520. In symbols, what is p(M>520)?
C. What is the probability that the sample mean will be between M=510 and M=520? In symbols, what is p(510<M<520)?

4. People are selected to serve on juries by randomly picking names from the list of registered voters. The average age is µ=39.7 years with a standard deviation of ?=12.4. A statistician randomly selects a sample of n=16 people who are currently serving on juries. The average age for the individuals in the sample is M=48.9 years.
A. How likely is it to obtain a random sample of n=16 jurors with an average age greater than or equal to 48.9?
B. Is it reasonable to conclude that this set of n=16 people is not a representative random sample of registered voters?

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Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.