Probability, Random Variables, and Probability Distributions

If the weights of pumpkins in a patch are normally distributed with a mean of 10 pounds and a standard deviation of 2 pounds, what would be the new standard deviation if we were to quadruple every pumpkin's weight?

What would be the standard deviation for the discrete random variable representing flipping a fair coin three times and counting heads?

What does the standard deviation of a random variable measure?

What kind of study involves observing subjects without influencing them?

In a set containing x data points whose values range from minimum value $x_{ ext{min}}$ to maximum value $x_{ ext{max}}$, using standardized score transformation ext{SSC} = rac{x_i - x_{ ext{min}}}{x_{ ext{max}} - x_{ ext{min}}}, what would SSC be for a point exactly halfway between the min and max?

What does the Central Limit Theorem state?

A store owner records sales in dollars from Monday through Friday with values $150,$ 120, $160,$ 110, and $ 130 respectively; what's their approximate combined mean and standard deviation?

A school survey asks students to rate their satisfaction with lunch options on a scale of –10. When analyzing the data, they find the responses are modeled by a symmetric bell-shaped curve centered at a rating of 0. Which of the following describes the relationship between the median and the average ratings?

What is the mean of a discrete random variable X that takes on values 2, 4, and 6 with probabilities 0.2, 0.5, and 0.3 respectively?

A game show contestant can either win $500 or lose$200 when spinning a wheel depending on where it lands; given that both outcomes are equally likely, what is this game's expected payoff?