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Probability Distributions and Sampling Scenarios Explained

Learn about sampling distributions, probabilities, and the impact of various factors on outcomes in statistical scenarios.

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Probability Distributions and Sampling Scenarios Explained

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  1. The average age of a vehicle registered in the United States is 96 months. Assume the standard deviation is 16 months. If a random sample of 36 cars is selected, find the probability that the mean of their age is between 90 and 100 months.

  2. Sampling Distribution of Sample Proportions

  3. General Properties • Approximately normal if

  4. Proportion of all cardiac patients receiving blood transfusions who contract hepatitis was 0.07. A new screening is believed to reduce this incidence rate. It’s given to 200 blood recipients. What’s the probability that less than 6 of the 200 contract hepatitis.

  5. Assume that 30% of students at a university wear contact lenses. We randomly select 100 students. What is the probability that more than one-third of this sample wear contacts?

  6. The library says that 60% of people like to read murder mysteries. What’s the probability that at least 32 out of 60 people will prefer to read a murder mystery?

  7. A school claims that 98% of its students pass the exit exam. What's the probability that less than 96% of the 100 students that takes the exam passes the test.

  8. The average price of a pound of bacon is $2.02. Assume the standard deviation is $0.08. If a random sample of 40 one-pound packages is selected, find the probability that the mean of the sample will be less than $2.00.

  9. Approximately 62% of all freshmen loose their Life scholarship by the end of their sophomore year. What’s the probability that in a group of 40, more than 26 have lost their life scholarship.

  10. Homework • Worksheet

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