- Given the following sample of 10 high temperatures from March: 55, 60, 57, 43, 59, 66, 72, 65, 59, 47.

- Determine the mean.
- Determine the median.
- Determine the mode.
- Describe the shape of the distribution.
- Determine Q1, Q2, Q3 and IQR.

- The contingency table shows classification of students in a Statistics class.

From NJ | From PA | ||

GPA at least 3.0 | 15 | 5 | 20 |

GPA below 3.0 | 45 | 35 | 80 |

60 | 40 | 100 |

- If a student is selected at random, what is the probability that he/she is from NJ?
- If a student is selected at random, what is the probability that he/she has a GPA below 3.0?
- If we know that the student is from PA, what is the probability that he/she has a GPA of at least 3.0?
- If a student is selected at random, what is the probability that he/she is from NJ and has a GPA below 3.0.
- If a student is selected at random, what is the probability that he/she from PA and has GPA of at least 3.0.

- Your friend is applying for 4 jobs. The hourly pay rate for the 4 jobs are, $8, $12, $15, $20. The probability distribution below shows the probability of getting each of these jobs:

Job Pay Rate, X | Probability, P(X) |

8 | .30 |

12 | .20 |

15 | .40 |

20 | .10 |

- What is the probability that your friend will get a job paying at least $15/hour?
- What is the expected pay rate for your friend?

- It is known that 31% of cars are considered gas hogs (i.e. they give less than 15 mpg). If we select 20 cars at random:
- What is the probability that exactly 4 will be gas hogs?
- What is the probability the at least 4 but not more than 7 will be gas hogs?
- How many cars are most likely to be gas hogs?

- You ask all 200 students at school how much money they have in their pockets. The amount ranges from $0 to $130. You determine the mean to be $56.40 with standard deviation of $8.40. You believe that the amount is normally distributed.
- If you pick a person at random, what is the probability that he/she has at least $45?
- What percentage of the students will have between $40 and $50 in their pockets.
- If you pick a person at random, what is the probability that he/she has either less than $30 or more than $70.
- Approximately how many people in the class do you expect to have at least $65?
- We want to identify the students with top 10.5% amounts as “rich”. What is the minimum dollar amount the students in this group would need in their pockets.

- Assume that on the third exam in a calculus course, the average score over the years has been 72 with a standard deviation 12. You are currently taking the course and there are 25 students in the class?

- What is the probability that the mean score for your class will be greater than 75?
- What is the probability that the mean score for your class will be between 68 and 70?

- A sample of 25 days in summer yields an average high temperature of 80 with a standard deviation of 12.
- Give a point estimate of the true mean of the high temperature.
- Find a 99% confidence interval for the average high temperature for the summer.
- How big a sample do we need if we want to be 90% confident of being within 7 degrees of the population mean?

- A sample of 100 exams yielded an average grade of 82 and standard deviation of 14. Find a 95% confidence interval for the average exam grade.
- Heights of aliens from Mars are known to be normally distributed with a population standard deviation of 9 inches. How big a sample do we need to take if we want be 95% confident that our error will not exceed 3 inches?
- Preliminary studies have shown that 20% of the voters might be willing to vote for Sran for President.
- Construct a 90% confidence interval for the proportion of voters who would be willing to support Sran.
- Before entering the race, Sran would like to conduct a poll to check his level of support. How big should be the sample be if he wants to be 95% sure that the error is no more than 2%?

- The average weight of men joining a gym has historically been 170 pounds with a standard deviation of 27. The owner feels that the average weight has now decreased to less than 165 pounds. To support his claim, the owner conducts a sample of 25 men and finds their average to be 153. He would like to use a significance level of .05 to test his claim.
- State the null hypothesis.
- State the alternate hypothesis.
- Will you use z or t distribution for this problem?
- Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
- Determine the critical value.
- Determine the rejection region.
- Calculate the test statistic.
- Would you accept or reject the owner’s claim? Explain.

- The average score on a certain college entrance test has been known to be 240. The dean of a university feels that this has changed.He conducts a sample of 25 students to test his claim. The sample yields an average of 232 with a standard deviation of 25. He would like to use a significance level of .10.
- State the null hypothesis.
- State the alternate hypothesis.
- Will you use z or t distribution for this problem?
- Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
- Determine the critical value.
- Determine the rejection region.
- Calculate the test statistic.
- Would you accept or reject the dean’s claim?

- A presidential candidate states that she currently has exactly 30% of the vote. A newspaper thinks that this number is inaccurate. So it conducts a sample 500 voters and finds 175 people support the candidate. The newspaper would like to test its claim using .05 significance level.
- State the null hypothesis.
- State the alternate hypothesis.
- Will you use z or t distribution for this problem?
- Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
- Determine the critical value.
- Determine the rejection region.
- Calculate the test statistic.
- Would you accept or reject the newspaper’s claim?