Question

Check my work mode: This shows what is correct or Incorrect for the work you have completed so far. Iit does not Indicate comple 3 Berdine's Chicken Fectory has several retail stores. When Interviewing applicants for server positions, the owner would lke to include information on the amount of tip a server can expect to earn per bill A study of 500 recent bilis Indicated the server eamed the following tips: 25 under ss s up to under 10 10 up to under 20 20 up to under 50 Total a. What is the probability of a tip of $50 or more? (Round the final answer to 2 decimal places Probability b. Are the categories "$0 to under $5. "$5 to unde $10," and so on considered mutualy exclusive? c. If the probabilities associated with each outcome were totalled, what would that total be? Probability d. Whet is the probability of a tp of up to $10? (Round the final answer to 2 decimal places.) Probability e. Whet is the probability of a tip of less than $50? (Round the final answer to 2 declmal places) Probablity MacBook Air

Answer 1

Formula of Probability = $\frac{NumberOf Favorable Outcome}{Total Possible Outcome}$

(a) Here, given a tip of $50 or more for number of bills 50 out of 500 .

That means, we have favorable outcome = 50

and Total number of outcomes = 500

$\implies$P(of a tip of $50 or more) = $\frac{50}{500} = \frac{1}{10}$ $=$   $0.10$

(b) Mutually Exclusive : When the lower limit of a class interval is included but upper limit of a class interval is excluded then this type of intervals are mutually exclusive .

Here, we can see the upper class intervals are not included thus it is a case of Mutually Exclusive .

(c) P($0 up to under $5) = $\frac{200}{500} = \frac{2}{5}$

P($5 up to under $10) = $\frac{100}{500} = \frac{1}{5}$

P($10 up to under $20) = $\frac{75}{500} = \frac{3}{20}$

P($20 up to under $50) = $\frac{75}{500} = \frac{3}{20}$

P($50 or more) = $\frac{50}{500} = \frac{1}{10}$

and summing of all Probabilities = $\frac{2}{5} + \frac{1}{5} + \frac{3}{20} + \frac{3}{20} + \frac{1}{10} = 1$

(d) Now, we have to find probability (of a tip of up to $10) = P($ 0 up to under $5) + P($5 up to under$10) + P(of a tip of exactly $10) .

(Since , the given intervals between class limits are continuous and also these are mutually exclusive)

Now, P( of a tip of exactly $10) = $F_{X}(x) - F_{X}(x^{-})$

Here, $F_{X}(x)$ is sum of probability up to under $10 and $F_{X}(x^{-})$ is the probability of up to under a very short gap which exceeding to $10.

$\implies$P(of a tip of exactly $10) = $F_{X}(10) - F_{X}(10^{-})$

$\implies$P(of a tip of exactly $10) = $\frac{15}{20} - \frac{3}{5} = \frac{3}{20}$

Now, Probability (of a tip of up to $10) = P($ 0 up to under $5) + P($5 up to under$10) + P(of a tip of exactly $10) .

$\implies$ Probability (of a tip of up to $10) =   $\frac{2}{5} + \frac{1}{5} + \frac{3}{20} = \frac{15}{20} = \frac{3}{4}$  $= 0.75$

(e) Now, Probability (of a tip less than $50) = Sum of all probability up to under $50 =   $\frac{2}{5} + \frac{1}{5} + \frac{3}{20} + \frac{3}{20} = \frac{18}{20} = 0.90$ .