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ECON 230 Test 2 Review Sheet: Probability and Statistics, Exams of Statistics

A review sheet for test 2 in econ 230, focusing on probability distributions, mean and standard deviation, sampling distributions, and confidence intervals. It includes reading materials from chapters 5, 6, 7, and 8, as well as important terms and phrases. The document also provides solutions to various problems.

Typology: Exams

Pre 2010

Uploaded on 08/13/2009

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koofers-user-n6f 🇺🇸

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ECON 230
TEST 2 REVIEW SHEET
Readings the test will cover:
Chapter 5: Sections 5.1-5.4, 5.8
Chapter 6: Sections 6.1-6.6
Chapter 7:
Chapter 8: Sections 8.1-8.4
Important terms and phrases:
Chapters 5 and 6:
- Discrete random variable
- Discrete probability
distribution
- Poisson probability
distribution
- Continuous random
variable
- Continuous probability
distribution
- Normal distribution
- Standard normal
distribution
- Area under the normal
curve
- Finding z- and x-values
- Using probability tables
- Sampling distribution of a
sample mean
- Mean and standard
deviation of a sample mean
Chapter 7:
- Population distribution
- Sampling distribution
- Sampling error
- Mean and standard
deviation of
x
- Shape of the sampling
distribution of
x
- Central limit theorem
- Population proportion
- Sample proportion
Chapter 8:
- Point estimate
- Margin of error
- Confidence interval
- Confidence and
significance levels
- Estimating confidence
intervals when
is known
- Estimating confidence
intervals when
is not
known
- t – distribution
1. A publisher introduces a new weekly magazine for teenagers. The company’s marketers estimate
that the sales x (in thousands) will be approximated by the following distribution.
a) Check whether the given distribution is a probability distribution.
b) If it is a probability distribution, find the mean for this distritbution.
c) If it is a probability distribution, find the standard deviation.
2. Problem 5.94. Replace part b) with the following question:
b) What is the probability that Borok’s Electronics Company receives at least two applications in
xP(x)
10 .200
15 .300
20 .150
25 .350
1
pf3

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ECON 230

TEST 2 REVIEW SHEET

Readings the test will cover: Chapter 5: Sections 5.1-5.4, 5. Chapter 6: Sections 6.1-6. Chapter 7: Chapter 8: Sections 8.1-8. Important terms and phrases: Chapters 5 and 6:

  • Discrete random variable
  • Discrete probability distribution
  • Poisson probability distribution
  • Continuous random variable
    • Continuous probability distribution
    • Normal distribution
    • Standard normal distribution
    • Area under the normal curve
      • Finding z - and x -values
      • Using probability tables
      • Sampling distribution of a sample mean
      • Mean and standard deviation of a sample mean Chapter 7: - Population distribution
  • Sampling distribution
  • Sampling error
    • Mean and standard deviation of x
    • Shape of the sampling distribution of x
      • Central limit theorem
      • Population proportion
      • Sample proportion Chapter 8:
  • Point estimate
  • Margin of error
  • Confidence interval
    • Confidence and significance levels
    • Estimating confidence intervals when^ ^ is known
      • Estimating confidence intervals when^ ^ is not known
      • t – distribution 1. A publisher introduces a new weekly magazine for teenagers. The company’s marketers estimate that the sales x (in thousands) will be approximated by the following distribution. a) Check whether the given distribution is a probability distribution. b) If it is a probability distribution, find the mean for this distritbution. c) If it is a probability distribution, find the standard deviation. 2. Problem 5.94. Replace part b) with the following question: b) What is the probability that Borok’s Electronics Company receives at least two applications in x P( x )

a week?

3. A package of frozen vegetables has a label that says “contents 32 oz.” However, the company that produces these packages knows that the weights are normally distributed with mean 32 oz. and standard deviation 2 oz. If a package is chosen at random, what is the probability that it will weigh a) more than 35 oz.? b) less than 30 oz.? c) between 30 and 35 oz.? 4. Suppose that the test scores for a college entrance exam are normally distributed with a mean of 450 and a standard deviation of 100. a) What percentage of those taking the exam score between 350 and 450? b) A student scoring above 400 is automatically admitted. What percent score above 400? c) The upper 5% receive scholarships. What score must a student make on the exam to receive a scholarship? 5. The heights of adult males are normally distributed with a mean height of 70 inches and a standard deviation of 2.6 inches. How high should the doorway be constructed so that 90% of the men can pass through it without having to bend? 6. The heights of college age men are known to be normally distributed with a mean of 68 in. and a standard deviation of 3 in. a) What is the probability that the mean height of a random sample of nine college men is between 67 and 69 inches? b) What is the probability that the mean height of a random sample of 100 college men is between 67 and 69 inches? c) Compare your answers to parts a and b. Was the probability in part b much higher? Why would you expect this? 7. According to Bride’s Magazine , the cost of a wedding these days can be expensive when the costs of the reception, engagement ring, bridal gown, and pictures-just to name a few- are included. Shao Wei wants to estimate the mean cost for a wedding. From a random sample of 115 recent U.S. weddings, the mean cost was $18,945 and the standard deviation was $8,280. Construct a 99% confidence interval for the population mean cost for a wedding. 8. In a survey of 2000 adults from the U.S. age 65 and over, 1320 received a flu shot. a) Find a point estimate for the population proportion p of adults receiving a flu shot. b) Construct a 90% confidence interval for the population proportion. 9. An economist wants to estimate the mean income for the first year of work for college graduates. Determine the minimum required sample size to construct a 95% confidence interval such that the confidence interval goes from $500 below the mean to $500 above the mean. Assume that the population standard deviation is $6250.