What percent of people make less than $25000?

Transcription

1 ` Problem of the Day The mean income for a year old in the State of Illinois is around $39000 with a standard deviation $4670. (Assume incomes are normally distributed) What percent of people make more than $45000? What percent of people make less than $25000?

2 Problem of the Day You predict that 73% of students feel that the school lunch is acceptable. You want to confirm your "feeling" by randomly sampling 40 students. Find the probability your sample finds less than 70% of students feel that the lunch is acceptable.

3 Problem of the Day You predict that 73% of students feel that the school lunch is acceptable. You want to confirm your "feeling" by sampling 40 students. Find the probability your sample finds less than 70% of students feel that the lunch is acceptable.

4 Rolling Die Simulation Your simulation will involve 20 "rolls" of a single die. You will want to see the number of evens you "roll" in your 20 "rolls". One of your group members will enter your 3 values in the spreadsheet and the mean of your 3 numbers.

5 Chapter 18 Sampling Distribution Models we want to answer questions using our sample when we are given population parameters Sampling Distributions(Proportions or Means) have assumptions and conditions we need in order to use sampling error(sampling variability)

6 Assumptions sample values must be independent sample size must be large enough Conditions(Proportions) for using the Normal model to approximate(check) Randomization:needs to be a representative sample 10% condition:sample is no larger than 10% of population Success/Failure:np and nq>

7 Sampling Distribution Model based on our actual parameters and sample need to find a mean and standard deviation

8 Mean Standard Deviation

9 Of all cars on the interstate, 80% exceed the speed limit. What proportion of speeders might we see among the next 50 cars?

10 We don t know it, but 52% of voters plan to vote Yes on the upcoming sales tax increase. We poll a random sample of 300 voters. What might the percentage of yes voters appear to be in our poll?

11 The Centers for Disease Control say that about 25% of high school students use tobacco(down from a high of over 40% in 1997). Suppose you randomly select highschool students to survey them on their attitudes toward scenes of smoking in the movies. What s the probability that d) what is the probability that more than 70 of the 250 seniors uses tobacco on a regular basis?

12 Groovy M&M s are supposed to make up 30% of the candies sold. In a large bag of 250 M&M s, what is the probability that we get at least 25% groovy candies?

13 Groovy M&M s are supposed to make up 30% of the candies sold. In a large bag of 250 M&M s, what is the probability that we get at least 25% groovy candies?

14 Sampling Distributions for Sample Means (Central Limit Theorem) always approximates Normal distribution as long as Sample is large enough, Independent, Randomized collection this is true whether the population has a normal distribution or not

15 Assumptions sample values must be independent sample size must be large enough Conditions(Means) for using the Normal model to approximate(check) Randomization:needs to be a representative sample 10% condition:sample is no larger than 10% of population Sample is Large Enough

16 Mean: equals population mean, y = Standard deviation:

17 Speeds of cars on a highway have mean 52 mph and standard deviation 6 mph, and are likely to be skewed to the right (a few very fast drivers). Describe what we might see in random samples of 50 cars. Use the Rule to help.

18 SAT scores should have mean 500 and standard deviation 100. What about the mean of random samples of 20 students? What about the standard deviation?

19 At birth, babies average 7.8 pounds, with a standard deviation of 2.1 pounds. A random sample of 34 babies born to mothers living near a large factory that may be polluting the air and water shows a mean birth weight of only 7.2 pounds. Is that unusually low?

20 Practice Problems A particular candidate for City Council is favored by 48% of voters. A certain polling agency will take a random sample of 200 people. If a simple majority will win the election what is the probability that the candidate wins?

21 Practice Problems A national survey found that 61% of high school graduates go on to receive 2 year or 4 year degrees. In California, the percentage is 55%. If this proportion was based on a random sample of 400 California High School students, is this unusually low?(be sure to check your assumptions)

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23 Practice Problems The average wait time for an elevator is.5 minutes with a standard deviation of.289 minutes. Describe the distribution of the population and then find the probability that a sample of 16 people waits more than 45 seconds for an elevator.

24 Readings and Examples pgs Homework pgs :1,3,5,7,11,25,29,33,37,43,49

25 Exit slip On a half sheet of paper... The average composite ACT score for Ohio students who took the test in 2003 was Assume that the standard deviation is In a random sample of 25 students who took the exam in 2003, what is the probability that the average composite ACT score is 22 or more? (Make sure to check all necessary conditions.)

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