Question

2. Calculate and interpret probabilities for a discrete variable from a table.

Example:
x
The following probability distribution gives the number of people waiting in line, x, at a fast-food
restaurant on any given day at lunchtime:
P(x)
0
1
0.02 0.02
2
0.05
3
0.25
4
0.19
5
0.17
6
0.13
7
0.10
8
0.07
a. Interpret the probability of there being at most 2 people waiting in-line at this fast-food
restaurant at lunchtime on any given day using the format discussed in the video lessons.
b. Would it be unusual for there to be at least 5 people waiting in-line at this fast-food
restaurant at lunchtime on any given day? Explain how you can tell and/or calculate
the necessary numbers to help you answer this question.
c. Calculate the mean and standard deviation of the values of x in this probability table
Using R.
d. Interpret the mean value.

Answer 1

To interpret probabilities from a table, you sum relevant probabilities for certain outcomes. The mean represents the expected average number, and it can be found alongside standard deviation using formulas in R. It's not unusual to see at least 5 people in line as the probability is significant for that outcome.

option a is the correct

Step-by-step explanation:

To calculate and interpret probabilities for a discrete variable from a probability table, you assess the likelihood of different outcomes based on provided probabilities. For the provided discrete probability distribution of the number of people waiting in line at a fast-food restaurant, we can find and interpret various probabilities:

• The probability of there being at most 2 people waiting in-line can be found by summing the probabilities for 0, 1, and 2 people. It is P(0) + P(1) + P(2) = 0.02 + 0.02 + 0.05 = 0.09.
• It would not be unusual for there to be at least 5 people in line at lunchtime since the combined probability for 5 or more people (P(5) + P(6) + P(7) + P(8)) is relatively high.
• To calculate the mean (μ) and standard deviation (σ) of the values of x in R, one would use the sum and sqrt functions along with the probabilities to compute these statistics based on the formulas for mean and standard deviation of discrete variables.

The mean value represents the expected average number of people in line. You can interpret this number as the average number of people you would expect to see in line at lunchtime over many days.