# Statistics - Probability Distribution

Can you help me specifically with Part B - especially #3 & #4?

Part A Directions: Using 100 pennies, complete the following activities:

1. Spread 100 pennies across a table

2. Separate into two groups based on heads and tails

3. Total the number of heads and number of tails

4. Compute the percentage of heads and the percentage of tails

5. Create a bar chart to show results

Part B Directions: Using 100 pennies, complete the following activities:

1. Group pennies by year

2. Regroup pennies into various classes by decades

3. Create a relative frequency distribution by decades (see Excerpt 7.1 from Research in Education: Evidence-Based Inquiry for a model; focus on the percent column) page 150 (3 of 29)

4. Create a cumulative frequency distribution by decades (see Excerpt 7.1 from Research in Education: Evidence-Based Inquiry for a model; focus on the percent summation column)

5. What is the relative frequency of the 3rd class?

6. What is the cumulative frequency of the 5th class?

7. Create a histogram based on the cumulative frequency distribution (see Excerpt 7.4 from Research in Education: Evidence-Based Inquiry for a model)

8. What percent of the coins are 1970 or older?

[See the attached Question File.]

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#### Solution Summary

Neat, step-by-step solutions to all the problems uisng graphs, histograms are provided.

Statistics: Probabilities of normal distribution of ACT scores; poll for education vouchers

1. The scores of students on the ACT college entrance examination in a recent year had a

normal distribution with a mean of 18.6 and a standard deviation of 5.9. A simple random

sample of 60 students who took the exam is selected for study:

a) What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample mean score for samples of size 60?

b) What is the probability that the sample mean is 20 or higher?

c) What is the probability that the sample mean falls within 2 points of the population mean?

d) What value does the sample mean have be in order for it to be in the top 1% of the sampling distribution?

2. Last year, a national opinion poll found that 43% of all Americans agree that parents should be given vouchers good for education at any public or private school of their choice. Assume that in fact the population proportion is 0.43. A random sample of 350 is to be selected and asked the same question.

a) What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample proportion for samples of size 350?

b) What is the probability that the sample proportion will fall within 0.03 of the population proportion?

3. Redo part (b) of problem 2, but assume that the sample size is 700. Does this answer make sense when compared to #2, part (b)? Why?

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