# 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.

https://brainmass.com/math/graphs-and-functions/calculating-probabilities-assuming-normal-distribution-551743

#### 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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A company examines homeowners records and sees that the mean loss from wind annually is $250 per house with std dev of $1000. They plan to sell wind insurance for $250 + estimates coverage costs & profits.

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iii) Why it would be unwise to sell 12 policies or less.

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