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Berdine’s Chicken Factory has several stores in the Hilton
Chapter 5, Problem 44E(choose chapter or problem)
Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift.
\(\begin{array}{|lc|}
\hline \text { Amount of Tip } & \text { Number } \\
\hline \$ 0 \text { up to } \$ 20 & 200 \\
20 \text { up to } 50 & 100 \\
50 \text { up to } 100 & 75 \\
100 \text { up to } 200 & 75 \\
200 \text { or more } & \underline{50} \\
\text { Total } & 500 \\
\hline
\end{array}\)
a. What is the probability of a tip of $200 or more?
b. Are the categories " $0 up to $20”, “$20 up to $50," and so on considered mutually exclusive?
c. If the probabilities associated with each outcome were totaled, what would that total be?
d. What is the probability of a tip of up to $50 ?
e. What is the probability of a tip of less than $200 ?
Questions & Answers
QUESTION:
Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift.
\(\begin{array}{|lc|}
\hline \text { Amount of Tip } & \text { Number } \\
\hline \$ 0 \text { up to } \$ 20 & 200 \\
20 \text { up to } 50 & 100 \\
50 \text { up to } 100 & 75 \\
100 \text { up to } 200 & 75 \\
200 \text { or more } & \underline{50} \\
\text { Total } & 500 \\
\hline
\end{array}\)
a. What is the probability of a tip of $200 or more?
b. Are the categories " $0 up to $20”, “$20 up to $50," and so on considered mutually exclusive?
c. If the probabilities associated with each outcome were totaled, what would that total be?
d. What is the probability of a tip of up to $50 ?
e. What is the probability of a tip of less than $200 ?
ANSWER:Step 1 of 5
Given a study of 500 recent checks indicated the server earned.
Then the table is given below.
|
Amount of Tip |
Number |
|
$0 up to $ 20 |
200 |
|
$20 up to $50 |
100 |
|
$50 up to $100 |
75 |
|
$100 up to $200 |
75 |
|
$200 or more |
50 |
|
Total |
500 |
Our goal is:
a). We need to find the probability of a tip of $200 or more.
b). We need to find are the categories mutually exclusive.
c). We need to find the total probability.
d). We need to find the probability of a tip of up to $50.
e). We need to find the probability of less than $200.
a). Now we have to find the probability of a tip of $200 or more.
From the above table the amount tip $200 or more = 50 (Number) and
The total number of amount tip is 500.
Then the probability of tip of $200 or more is
P (tip of $200 or more) = \(\frac{50}{500}\)
P (tip of $200 or more) = 0.1
Therefore, the probability of tip of $200 or more is 0.1.