5.38 Tomato as a taste modifier. Miraculin-a protein naturally produced in a rare tropical fruit-can convert a sour taste into a sweet taste; thus, it has the potential to be an alterna- tive low-calorie sweetener. In Plant Science (May 2010), a of Japanese environmental scientists investigated the group ability of a hybrid tomato plant to produce miraculin. For a particular generation of the tomato plant, the amount x of miraculin produced (measured in micrograms per gram of fresh weight) had a mean of 105.3 and a standard deviation of 8.0. Assume that x is normally distributed. a. Find P(x > 120). b. Find P(100 < x < 110). c. Find the value a for which P(x < a) = .25.

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Transcription for Educational Website:

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**Modified Dental Anxiety Scale**

Using the Modified Dental Anxiety Scale (MDAS), a random sample of adults was studied to assess levels of dental anxiety. The scoring range is from 0 (no anxiety) to 25 (extreme anxiety), with an average score of 11 and a standard deviation of 4. It is assumed that scores follow a normal distribution with a mean (μ) of 11 and standard deviation (σ) of 4.

**Tasks:**

a. Calculate the z-value for a score of 10.  
b. Determine the probability that a score falls between 10 and 15.  
c. Find the probability for scores greater than 20.

---

**5.38 Tomato as a Taste Modifier**

Miraculin, a protein from a rare tropical fruit, can convert sour tastes to sweet, potentially serving as a low-calorie sweetener. A Japanese environmental study investigated a hybrid tomato's miraculin production, yielding an average of 105.3 micrograms per gram fresh weight, with a standard deviation of 8. Assume a normal distribution.

**Tasks:**

a. Compute the probability P(x > 120).  
b. Find P(100 < x < 110).  
c. Determine the value of 'a' where P(x < a) = 0.25.

---

**5.39 Deep Mixing of Soil**

Deep mixing is a method for improving soft soils like clay, silt, and peat, using lime-cement columns. Swedish engineers tested the method’s effectiveness on soil properties in the journal "Giorisk" (Vol. 7, 2013). The procedure involves a rod with a cone tip, measuring cone penetration resistance in megapascals (MPa), following a normal distribution with a mean of 2.2 MPa.

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This detailed explanation of research studies and their findings can provide valuable insights into practical applications and theoretical calculations for educational purposes.
Transcribed Image Text:Transcription for Educational Website: --- **Modified Dental Anxiety Scale** Using the Modified Dental Anxiety Scale (MDAS), a random sample of adults was studied to assess levels of dental anxiety. The scoring range is from 0 (no anxiety) to 25 (extreme anxiety), with an average score of 11 and a standard deviation of 4. It is assumed that scores follow a normal distribution with a mean (μ) of 11 and standard deviation (σ) of 4. **Tasks:** a. Calculate the z-value for a score of 10. b. Determine the probability that a score falls between 10 and 15. c. Find the probability for scores greater than 20. --- **5.38 Tomato as a Taste Modifier** Miraculin, a protein from a rare tropical fruit, can convert sour tastes to sweet, potentially serving as a low-calorie sweetener. A Japanese environmental study investigated a hybrid tomato's miraculin production, yielding an average of 105.3 micrograms per gram fresh weight, with a standard deviation of 8. Assume a normal distribution. **Tasks:** a. Compute the probability P(x > 120). b. Find P(100 < x < 110). c. Determine the value of 'a' where P(x < a) = 0.25. --- **5.39 Deep Mixing of Soil** Deep mixing is a method for improving soft soils like clay, silt, and peat, using lime-cement columns. Swedish engineers tested the method’s effectiveness on soil properties in the journal "Giorisk" (Vol. 7, 2013). The procedure involves a rod with a cone tip, measuring cone penetration resistance in megapascals (MPa), following a normal distribution with a mean of 2.2 MPa. --- This detailed explanation of research studies and their findings can provide valuable insights into practical applications and theoretical calculations for educational purposes.
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