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# Probability - Statistics - Standard - Deviation

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1. In previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.84 inches. In a test sample of 40 new balls, the bounce heights had a mean of 92.67 inches and a standard deviation of 1.79 inches. Use a 0.05 significance level to determine whether there is sufficient evidence to support the claim that the new balls have bounce eights with a mean different from 92.84 inches. For this problem, the critical value of the statistic is?

2. Use the Poisson distribution to find the indicated probabilities. In one year, there were 116 homicide deaths in Richmond, Virginia. For a randomly selected day, find the probability that the number of homicide deaths is 0.

3. As part of the National Health and Nutrition Examination Survey, self-reported heights and measured heights were obtained for males aged 12 to 16.
The data are reported below:
Reported: 68 71 63 70 71 60 65 64 54 63 66 72
Measured: 67.9 69.9 64.9 68.3 70.3 60.6 64.5 67.0 55.6 74.2 65.0 70.8
Using a 0.05 significance level, the critical value of the statistic is?

4. A data set includes the heights of parents of 20 males. If the difference in height for each set of parents is found by subtracting the mother's height from the father's height, the result is a list of 20 values with a mean of 4.4 inches and a standard deviation of 4.2 inches. Use a 0.01 significance level to test the claim the mean difference is greater than 0. Accept or reject the null hypothesis?

5. A recent survey of 4276 randomly selected households showed that 4019 of them had telephones. Use these survey results to test the claim that the percentage of households is greater than the 35% rate that was previously found. Use a 0.01 significance level. Accept or reject the Null Hypothesis?

6. Given a = .10, H1 is p > 0.18, find the critical z value. Assume the normal distribution applies

7. A recent survey of 4276 randomly selected households showed that 4019 of them had telephones. Use these survey results to test the claim that the percentage of households is greater than the 35% rate that was previously found. Use a 0.01 significance level. For this problem, the value of the test statistic is?

8. In previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.84 inches. In a test sample of 40 new balls, the bounce heights had a mean of 92.67 inches and a standard deviation of 1.79 inches. Use a 0.05 significance level to determine whether there is sufficient evidence to support the claim that the new balls have bounce eights with a mean different from 92.84 inches. For this problem, the value of the test statistic is?

9. A data set includes the heights of parents of 20 males. If the difference in height for each set of parents is found by subtracting the mother's height from the father's height, the result is a list of 20 values with a mean of 4.4 inches and a standard deviation of 4.2 inches. Use a 0.01 significance level to test the claim the mean difference is greater than 0. For this problem, the critical value of the statistic is?

10. A data set includes the heights of parents of 20 males. If the difference in height for each set of parents is found by subtracting the mother's height from the father's height, the result is a list of 20 values with a mean of 4.4 inches and a standard deviation of 4.2 inches. Use a 0.01 significance level to test the claim the mean difference is greater than 0. For this problem, the value of the test statistic is?

[See the attached questions file.]

https://brainmass.com/statistics/probability/probability-statistics-standard-deviation-197527

#### Solution Summary

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## Business Statistics: Mean, Standard Deviations

I could use some help with the following. Could you please explain how you get the answer to the following questions in detail please so I can compare them to mine? I do not understand my book very well and I want to make sure I understand them correctly before I turn them in. Thank you

My first question is;

The mean starting salary for college graduates in the spring of 2004 was \$36,280.
I am asking to assume the distribution of starting salaries follows the normal distribution with a standard deviation of \$3,300.

What percentage of the graduates has starting salaries?

a) Between \$35,000 and 45,000
b) More than \$45,000
c) Between \$40,000 and 45,000

My second question is;

I am ask to assume a binomial probability distribution with n=40 and (pi) =.55 and compute the following
a) The mean and standard deviation of random variable
b) The probability that X is 25 or greater
c) The probability that X is 15 or less
d) The probability that X is between 15 and 25 inclusive

My third question;

A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to the Los Angeles International Airport is \$18.00 and the standard deviation is \$3.50.

I am ask to select a sample of 15 fares and answer a and b. Please explain how you got your answer so I can compare it to mine.

a) What is the likelihood that the sample mean is btw \$17.00 and 20.00?
b) What must you assume to make the above calculation?

My last question;
Dr. Patton is a Professor of English. Recently he counted the number of misspelled words in a group of student's essays. For his class of 40 students, the mean number of misspelled words was 6.05 and the standard deviation 2.44 per essay.

I need help constructing a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.

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