Final answer:
Questions involve describing a random variable and finding probabilities associated with it in various contexts, all within the field of Mathematics at the High School level.
Step-by-step explanation:
The subject of each of these questions is Mathematics, and they all involve the concept of a random variable and its probability distribution. A random variable is a variable whose numerical values result from a random experiment. The level of these questions indicates they are most appropriate for High School students studying probability and statistics.
Regarding question 98, the random variable X can be described as the weight of a single small bag of candies from the selected sample. The mean weight (notated as μ) is two ounces, the sample standard deviation (notated as Sx) is 0.12 ounces, and the population standard deviation (notated as σ) is known to be 0.1 ounce.
To describe the random variable X theoretically, if it were regarding the number of DVDs rented by a customer, X would represent the number of DVDs rented. The probability of specific outcomes, such as renting three DVDs or at least four DVDs, would be determined by the probability mass function provided for the scenario.
If the question involves the random variable P', which is the proportion of households that have three cell phones, then the variable is approximated by a normal distribution with the given parameters. The actual calculation of probabilities would require applying the normal distribution formulas and standardizing the random variable if necessary.
For the problem involving a mother being awakened by her newborn's crying, you would first construct a probability distribution table based on the relative frequency of each event occurring. Then you would calculate probabilities for different scenarios using that table.
Lastly, when discussing the probability that a customer rents at most two DVDs, one would need to refer to the provided probability distribution for that particular question. The cumulative probability for X taking on a value of 0, 1, or 2 would give the desired outcome.