Question

1. about 50% of the time marissa packs a sandwich for her lunch. about 25% of the time marissa packs leftovers and about 25% of the time she does not pack a lunch and orders take - out instead. explain how you could use a standard 52 - card deck of cards to simulate what marissa eats for lunch on any given day.
2. nick tells his sister penny that he gets up when his alarm clock rings the first time (without pressing snooze) about 85% of the time. within the next month, penny takes a random sample of seven days and finds that on four of the days, nick gets up when his alarm clock rings the first time, but on the other three days, he continues to sleep after his alarm clock rings.

a. does penny have some evidence that nick is lying? explain.
b. does penny have proof that nick is lying? explain.

1. fran uses a simulation to estimate the probability that the sum of the values on three dice is 15 or higher. she rolls three dice 30 times and records the sum each time. the dotplot of her results is shown.

a. what does the single dot above the 5 represent?
b. based on frans simulation, what is the probability that the sum of the values on three dice is 15 or greater?
c. the true probability of getting a sum of 15 or greater with three dice is 0.0926. compare frans simulated probability and the true probability. what might account for the difference?

Explanation:

Question 3a

In a dot - plot, each dot represents a single trial. Here, the trial is rolling three dice. So, the single dot above 5 represents one instance (trial) where the sum of the values on the three dice was 5.

Fran's simulated probability is based on a relatively small number of trials (\(n = 30\)). In probability, as the number of trials \(n\) increases, the experimental (simulated) probability approaches the theoretical (true) probability. A small sample size can lead to more variability. For example, 30 trials is a limited number of times to roll three dice, and random fluctuations in the small number of trials can cause the simulated probability to deviate from the true probability.

Answer:

The single dot above the 5 represents one trial (rolling three dice) where the sum of the values on the three dice was 5.

Question 3b

Step - by - Step Format:

Step1: Count the number of favorable outcomes

Count the number of dots above 14, 15, and 16. There are \(3\) dots (1 dot above 14, 1 dot above 15, and 1 dot above 16)

Step2: Calculate the probability

The formula for probability in a simulation is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}\). The total number of trials \(n = 30\).
So, \(P=\frac{3}{30}\)
Simplify the fraction: \(\frac{3\div3}{30\div3}=\frac{1}{10}=0.1\)