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5. Commercial cherry trees produce fruit according to a normal distribution with an average of 90 cherries per tree and a standard deviation of 11 kg per tree. a. Label the horizontal axis appropriately on the Normal curve at right. b. What is the probability that a tree produces at least 95 kg of cherries? Shade the appropriate area in the figure, and then determine the proportion. c. What is the probability that a tree yields between 85 and

5. Commercial cherry trees produce fruit according to a normal distribution with an average of 90 cherries per tree and a standard deviation of 11 kg per tree. a. Label the horizontal axis appropriately on the Normal curve at right. b. What is the probability that a tree produces at least 95 kg of cherries? Shade the appropriate area in the figure, and then determine the proportion. c. What is the probability that a tree yields between 85 and

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem 5: Analysis of Cherry Tree Yields** Commercial cherry trees produce fruit according to a normal distribution with an average of 90 kg of cherries per tree and a standard deviation of 11 kg per tree. a. **Label the Horizontal Axis on the Normal Curve** - The horizontal axis on the normal distribution curve represents the weight of cherries in kilograms. Values range from 57 kg to 123 kg, with the mean positioned at 90 kg. b. **Probability of Producing at Least 95 kg of Cherries** - To find the probability that a tree produces at least 95 kg of cherries, observe the shaded area to the right of 95 kg on the curve. This represents the proportion of trees producing 95 kg or more. c. **Probability of Yield Between 85 and 105 kg** - Calculate the probability that a tree yields between 85 kg and 105 kg of cherries. This is depicted by the area under the curve between these two values. d. **Percentile for a Harvest of 80 kg** - Determine the percentile rank for a harvest of 80 kg. This involves finding the cumulative proportion of trees producing up to 80 kg of cherries. **Graph Explanation:** - The graph is a bell-shaped normal distribution curve. The peak is centered at 90 kg, the mean yield. Vertical lines at 95 kg and 105 kg indicate specific positions relevant for calculating probabilities. - Shaded regions quantify the respective probabilities for the questions, with the area corresponding to values above 95 kg shaded to the right, and between 85 kg and 105 kg shaded in between.
Transcribed Image Text:**Problem 5: Analysis of Cherry Tree Yields** Commercial cherry trees produce fruit according to a normal distribution with an average of 90 kg of cherries per tree and a standard deviation of 11 kg per tree. a. **Label the Horizontal Axis on the Normal Curve** - The horizontal axis on the normal distribution curve represents the weight of cherries in kilograms. Values range from 57 kg to 123 kg, with the mean positioned at 90 kg. b. **Probability of Producing at Least 95 kg of Cherries** - To find the probability that a tree produces at least 95 kg of cherries, observe the shaded area to the right of 95 kg on the curve. This represents the proportion of trees producing 95 kg or more. c. **Probability of Yield Between 85 and 105 kg** - Calculate the probability that a tree yields between 85 kg and 105 kg of cherries. This is depicted by the area under the curve between these two values. d. **Percentile for a Harvest of 80 kg** - Determine the percentile rank for a harvest of 80 kg. This involves finding the cumulative proportion of trees producing up to 80 kg of cherries. **Graph Explanation:** - The graph is a bell-shaped normal distribution curve. The peak is centered at 90 kg, the mean yield. Vertical lines at 95 kg and 105 kg indicate specific positions relevant for calculating probabilities. - Shaded regions quantify the respective probabilities for the questions, with the area corresponding to values above 95 kg shaded to the right, and between 85 kg and 105 kg shaded in between.
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