Please Answer Questions On This Form:an Economist Says That

Please Answer Questions On This Form1an Economist Says That The Prob

Answer the following questions based on the provided scenarios and data:

Paper For Above instruction

1. An economist states that the probability is 0.47 that a randomly selected adult favors keeping the Social Security system as it is, 0.32 that the adult favors abolishing it completely, and 0.21 that the adult has no opinion or prefers other options. Determine whether these probabilities were obtained using the classical approach, the relative frequency approach, or the subjective probability approach.

2. In a sample of 300 adults, 111 like chocolate ice cream and 96 like vanilla ice cream. A single adult is chosen at random. Calculate:

• a. The probability that the adult likes chocolate ice cream, rounded to two decimal places.
• b. The probability that the adult likes vanilla ice cream, rounded to two decimal places.
• c. Whether these two probabilities sum to 1.0, rounded to two decimal places.

3. In a sample of 500 families:

• - 50 have a yearly income less than $50,000
• - 210 have a yearly income between $50,000 and $100,000
• - The remaining families earn more than $100,000.

Construct a frequency distribution table, calculate relative frequencies for each income class, and find the probabilities that a randomly selected family has an income less than $50,000 and more than $100,000.

4. Classify the following as either a discrete or a continuous random variable:

• a. The time remaining on a parking meter.
• b. The number of bats broken by a major league baseball team in a season.

5. Given a table of specific values of x and their probabilities, assess whether it represents a valid probability distribution.

6. Calculate P(x ≥ 4) for a given probability distribution of a discrete random variable x.

7. Calculate P(x ≥ 2) from a given probability distribution table.

8. Calculate P(1 ≤ x ≤ 4) for a given distribution.

9. Determine the mean and standard deviation for a specified probability distribution, providing the exact mean and rounding the standard deviation to three decimal places.

10. Identify which experiments among the listed are binomial, based on the nature of the trial and the outcome probabilities.

11. For a binomial experiment involving household purchases:

• a. State the possible integer values of the binomial random variable x representing households that have never purchased organic products in a sample of 10.
• b. Calculate the probability that exactly 6 households out of 10 have never purchased organic products, using the binomial probability formula, rounded to three decimal places.

Answer all questions with detailed explanations, calculations, and relevant justifications consistent with standard statistical practices.

References

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