
Concept explainers
Expand Your Knowledge: Geometric Distribution; Agriculture
Approximately
(a) Write out a formula for the
(b) Find the probabilities that
(c) Find the probability that
(d) What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use
Hint: See Problem 23.
(a)

The formula for the probability distribution of the random variable n.
Answer to Problem 24P
Solution: The required formula is
Explanation of Solution
Given: 3.6% of the Jonathan has bitter pit and n is a random variable, which shows that first Jonathan apple selected at random has bitter pit. So, the provided value is, p=0.036.
Calculation:
The random variable, n follows the geometric distribution with the probability of success,
The formula to calculate probability in geometric distribution is:
So, the formula of the probability distribution of the first apple selected has bitter pit can be found by using the above formula:
Thus, the formula of the probability distribution of the random variable n is
(b)

To find: The probability values for n=3, n=5 and n=12.
Answer to Problem 24P
Solution: The required values of probabilities are 0.03345, 0.0311 and 0.0241 respectively.
Explanation of Solution
Given: The provided values are p= 0.036 and n=3, 5 and 12.
Calculation:
The formula to calculate probability in geometric distribution is:
So, the probability that third Jonathan apple selected at random is the first one to have bitter pit can be calculated by using the geometric experiment formula:
The probability that fifth Jonathan apple selected at random is the first one to have bitter pit can be calculated by using the geometric experiment formula:
The probability that twelfth Jonathan apple selected at random is the first one to have bitter pit can be calculated by using the geometric experiment formula:
Interpretation: There is about 3.35%, 3.11% and 2.41% chance that
(c)

The probability that
Answer to Problem 24P
Solution: The estimated value of required probability is 0.8636.
Explanation of Solution
Given: The provided value is,
Calculation: The probability that
Now,
Interpretation: There is 86.36% chance that
(d)

The expected number of apples that are to be examined to find first one with bitter pit.
Answer to Problem 24P
Solution: The expected value is approximately 28.
Explanation of Solution
Given: 3.6% of the Jonathan has bitter pit. So, the provided value is,
Calculation:
The formula to calculate the expected value in geometric distribution is:
Now, substitute the provided value in the above formula as follows:
Therefore, the expected value is 28.
Want to see more full solutions like this?
Chapter 6 Solutions
Understanding Basic Statistics
- Name Harvard University California Institute of Technology Massachusetts Institute of Technology Stanford University Princeton University University of Cambridge University of Oxford University of California, Berkeley Imperial College London Yale University University of California, Los Angeles University of Chicago Johns Hopkins University Cornell University ETH Zurich University of Michigan University of Toronto Columbia University University of Pennsylvania Carnegie Mellon University University of Hong Kong University College London University of Washington Duke University Northwestern University University of Tokyo Georgia Institute of Technology Pohang University of Science and Technology University of California, Santa Barbara University of British Columbia University of North Carolina at Chapel Hill University of California, San Diego University of Illinois at Urbana-Champaign National University of Singapore…arrow_forwardA company found that the daily sales revenue of its flagship product follows a normal distribution with a mean of $4500 and a standard deviation of $450. The company defines a "high-sales day" that is, any day with sales exceeding $4800. please provide a step by step on how to get the answers in excel Q: What percentage of days can the company expect to have "high-sales days" or sales greater than $4800? Q: What is the sales revenue threshold for the bottom 10% of days? (please note that 10% refers to the probability/area under bell curve towards the lower tail of bell curve) Provide answers in the yellow cellsarrow_forwardFind the critical value for a left-tailed test using the F distribution with a 0.025, degrees of freedom in the numerator=12, and degrees of freedom in the denominator = 50. A portion of the table of critical values of the F-distribution is provided. Click the icon to view the partial table of critical values of the F-distribution. What is the critical value? (Round to two decimal places as needed.)arrow_forward
- A retail store manager claims that the average daily sales of the store are $1,500. You aim to test whether the actual average daily sales differ significantly from this claimed value. You can provide your answer by inserting a text box and the answer must include: Null hypothesis, Alternative hypothesis, Show answer (output table/summary table), and Conclusion based on the P value. Showing the calculation is a must. If calculation is missing,so please provide a step by step on the answers Numerical answers in the yellow cellsarrow_forwardShow all workarrow_forwardShow all workarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL




