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Statistics and Probability: Application of Concepts in Real-World Scenarios

An assignment on applying statistics and probability in real-life cases.

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    Statistics and Probability: Application of Concepts in Real - World Scenarios Part 1 Multiple Choice: The Gallup Poll interviewed 1423 randomly selected American citizens and reported that when asked which type of content bothers them most on TV, 44% identified ‘violence’. Answer the next two questions with this information. 1. Identify the population. a. 1423 b. American citizens c. Gallup poll d. 44% 2. The 44% that identified ‘violence’ as what bothered them the most from the sample of 1423 randomly selected American citizens is called a. a parameter b. a statistic c. Simpson’s paradox d. None of these above 3. Fill in the blank: The ________ of a variable tells us what values it takes and how often it takes these values. a. probability b. distribution c. population d. variable 4. 85% of the p hone calls to Regional Airways is for reservations . Suppose there were 100 calls to Regional Airways. Describe the distribution of the number of calls that were for re servation s out of the 100 . a. Normal distribution with mean = 100, standard deviation = 85. b. Binomial distribution with n = 100, p = 0.85. c. Binomial distribution with mean = 100, standard deviation = 85. d. Uniform distribution with n = 100, p = 0.85. The city gas mileage for 2001 vehicles has a mean μ = 21.2 miles per gallon and standard deviation σ = 5.4 MPG. Let X be the city MPG of 201 4 model year vehicles. Assume the gas mileage has an approximate Normal distribution. Answer the next two questions. 5. Find the probability that a vehicle chosen at random has a city MPG of 32 or higher. a. 0.02 b. 0.9772 c. 0.0228 d. 0.108 6. Suppose that a simple random sample of 36 vehicles were selected. What is the probability that the sample mean MPG, x , of these 36 vehicles is greater than 23 MPG?

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    a. 0.01 b. 0.8413 c. 0.9772 d. 0.0228 The table below shows quality ratings and the mean price from a sample of 300 restaurants located in the Los Angeles area. Use this information to answer the next three questions. Meal Price Quality Rating $10 – 19 $20 – 29 $30 – 39 $40 – 49 Total Good 42 40 2 0 84 Very Good 34 64 46 6 150 Excellent 2 14 28 22 66 Total 78 118 76 28 300 7. What is the percent of “Good” Quality Rating ? a. 28% b. 26% c. 53.8% d. 0% 8. What percent of the restaurants have a “Good” rating and has a meal price between $30 – 39? a. 2.4% b. 3% c. 0.67% d. 28% 9. What percent of the restaurants have an “Excellent” rating, given that the meal price is $40 – 49? a. 7.3% b. 78.6% c. 33.3% d. 22% Assume that 10% of people are le ft - handed. We randomly select 20 p eople at random. Answer the next two questions 10. What is the probability that exactly 5 out of the 20 people are left - handed? a. 0.25 b. 0.032 c. 0 d. 0.98875 11. What is the expected number of left - handed people out of the 20 randomly selected? a. 5 b. 10 c. 0.25 d. 2 0

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