A new restaurant is opening this March. The owner is deciding how to organize their lunch options (a choice of one sandwich and one salad) so that they can schedule their ingredient orders and ensure they have enough space for their inventory. Sandwiches cost either $12 or $15, while salads cost either $3, $5, or $7. Let R and S be discrete random variables representing the cost of sandwiches and salad, respectively. Based on market research of similar restaurants, the owner believes the joint pmf (representing probabilities of customers ordering each possible sandwich/salad pair) is as follows: R

Given that 20 students out of a total of 100 students passed their math exam, what is the 95% CI for the proportion of students that have passed? Round to 2 decimal places.

The t critical value for a 90% confidence interval and a sample size of 25 is 1.711.

If you need to have $9,000 in savings at the end of 4 years and your savings account yields 5% annual interest, how much do you need to deposit today? Note that answers are rounded to the nearest dollar. 

If you find a P value of 0.20 and your alpha value is 0.05, you will reject your null hypothesis.

A patient develops arm swelling after breast cancer surgery with lymph node removal. This is MOST consistent with:

You perform a two-tailed hypothesis test on your experimental data and end up with the following rejection region:

Researchers studying weight loss conducted a 3-month clinical trial to evaluate the efficacy of a new weight loss intervention. The experimental group (who received the intervention) with 57 participants had an average weight loss of 1.15 kg with a sample standard deviation of 0.41 kg. Develop a 95% confidence interval on the mean weight loss after 3 months  of this intervention. Assume the participants were randomly sampled and their weights are independently distributed. 

The 10 data points below refer to the daily number of flu shots given at a clinic at the end of January 2024. 19 27 20 22 18 2 12 15 21 11 What are the sample mean and median, respectively? 

The family of normal distributions are often a good approximation for many real-world random phenomena.