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.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
5.38
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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.
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**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.
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**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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