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Calculating Probabilities Assuming Normal Distribution

For the following answer True or False for each question
1. A population forms a normal distribution with µ=80 and ơ=10. In this population, 69.15% of the scores greater than x=75.
2. A population forms a normal distribution with µ=80 and ơ=10. In this population, 84.13% of the scores greater than x=90.
3. A population forms a normal distribution with µ=80 and ơ=10. In this population, 42.07% of the scores greater than x=78.
4. If one score is randomly selected from a normal distribution with µ=100 and ơ=20, the probability of obtaining a score greater than x=110 is 0.6915.
5. If one score is randomly selected from a normal distribution with µ=100 and ơ=20, the probability of obtaining a score less than x=95 is 0.4013.
6. If one score is randomly selected from a normal distribution with µ=100 and ơ=20, the probability of obtaining a score less than x=70 is 0.0013.
7. If one score is randomly selected from a normal distribution with µ=100 and ơ=20, the probability of obtaining a score between x=90 and x=100 is 0.3085.
8. If one score is randomly selected from a normal distribution with µ=100 and ơ=20, the probability of obtaining a score between x=80 and x=120 is 0.3413.
9. A vertical line drawn through a normal distribution at z=-0.75 will separate the distribution into two sections. The proportion in the smaller section is 0.2734.
10. If samples of size n=16 are selected from a population with µ=40 and ơ=8, the distribution of sample means will have an expected value of 40.
11. If samples of size n=16 are selected from a population with µ=40 and ơ=8, the distribution of sample means will have a standard error of 2 points.
12. The mean for a sample of n=4 scores has a standard error of 5 points. This sample was selected from a population with a standard deviation of ơ=20.
13. The mean for a sample of n=16 scores has an expected value of 50. This sample was selected from a population with a mean of µ=50.
14. On average, a sample of n=16 scores from a population with ơ=10 will provide a better estimate of the population mean than you would get with a sample of n=16 scores from a population with ơ=5.

Solution Preview

1. A population forms a normal distribution with µ=80 and ơ=10. In this population, 69.15% of the scores greater than x=75.
P(X>75)=P(Z>(75-80)/10)=P(Z>-0.5)=69.15%. True

2. A population forms a normal distribution with µ=80 and ơ=10. In this population, 84.13% of the scores greater than x=90.
P(X>90)=P(Z>(90-80)/10)=P(Z>1)=15.87%. False

3. A population forms a normal distribution with µ=80 and ơ=10. In this population, 42.07% of the scores greater than x=78.
P(X>78)=P(Z>(78-80)/10)=P(Z>-0.2)=57.93%. False

4. If one score is randomly selected from a normal distribution with µ=100 and ơ=20, the probability of obtaining a score greater than x=110 is 0.6915. ...

Solution Summary

The solution gives detailed steps on answerting 14 short questions regarding on probability calculation assuming the normal distribution. All questions are explained in details.

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