7.56 Example 7.18 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Sociochemosensory and Emotional Functions,” Psychological Science [2009]: 1118–1123). Suppose that instead of three shirts, each participant was asked to choose among four shirts and that the process was repeated five times. Then, assuming that the participant is choosing at random, x number of correct identifications is a binomial random variable with n = 5 and p = ¼.a. What are the possible values of x? b. For each possible value of x, find the associated probability p(x) and display the possible x values and p(x) values in a table.c. Construct a probability histogram for the probability distribution of x. **Example 7.56: Study on T-Shirt Identification Through Smell**A study, as described in Example 7.18, involved participants who were tasked with identifying which of three T-shirts had been worn by their roommate by smelling the shirts. The study, titled "Sociochemosensory and Emotional Functions," was published in *Psychological Science* in 2009 (pages 1118-1123). In this exercise, we explore a modification of the study where instead of three shirts, each participant chooses from four shirts. The process is repeated five times. Assuming random choice, let $ x $ represent the number of correct identifications. Here, $ x $ is a binomial random variable where $ n = 5 $ (number of trials) and $ p = \frac{1}{4} $ (probability of selecting the correct shirt at random).**Tasks:**a. **Determine the Possible Values of $ x $:** - The possible values for $ x $, representing the number of correct identifications out of five trials, range from 0 to 5.b. **Calculate and Display the Associated Probabilities $ p(x) $:** - For each value of $ x $, calculate the probability $ p(x) $ using the binomial probability formula: \[ p(x) = \binom{n}{x} p^x (1-p)^{n-x} \] - Construct a table listing each possible $ x $ and its corresponding probability $ p(x) $.c. **Construct a Probability Histogram:** - Create a histogram to visually represent the probability distribution of $ x $. Each bar corresponds to a possible value of $ x $ on the horizontal axis, with the height representing the probability $ p(x) $.This exercise will help illustrate concepts of probability distributions, specifically the binomial distribution, in a practical and engaging manner.

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Description: 7.56 Example 7.18 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Sociochemosensory and Emotional Functions,” Psychological Science [2009]: 1118–1123). Suppose

a. Obtain the possible values of x. It is given that each participant was asked to identify their…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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7.56 Example 7.18 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Sociochemosensory and Emotional Functions,” Psychological Science [2009]: 1118–1123). Suppose that instead of three shirts, each participant was asked to choose among four shirts and that the process was repeated five times. Then, assuming that the participant is choosing at random, x number of correct identifications is a binomial random variable with n = 5 and p = ¼.a. What are the possible values of x? b. For each possible value of x, find the associated probability p(x) and display the possible x values and p(x) values in a table.c. Construct a probability histogram for the probability distribution of x.

**Example 7.56: Study on T-Shirt Identification Through Smell**

A study, as described in Example 7.18, involved participants who were tasked with identifying which of three T-shirts had been worn by their roommate by smelling the shirts. The study, titled "Sociochemosensory and Emotional Functions," was published in *Psychological Science* in 2009 (pages 1118-1123).

In this exercise, we explore a modification of the study where instead of three shirts, each participant chooses from four shirts. The process is repeated five times. Assuming random choice, let $ x $ represent the number of correct identifications. Here, $ x $ is a binomial random variable where $ n = 5 $ (number of trials) and $ p = \frac{1}{4} $ (probability of selecting the correct shirt at random).

**Tasks:**

a. **Determine the Possible Values of $ x $:**

- The possible values for $ x $, representing the number of correct identifications out of five trials, range from 0 to 5.

b. **Calculate and Display the Associated Probabilities $ p(x) $:**

- For each value of $ x $, calculate the probability $ p(x) $ using the binomial probability formula:
\[
p(x) = \binom{n}{x} p^x (1-p)^{n-x}
\]
- Construct a table listing each possible $ x $ and its corresponding probability $ p(x) $.

c. **Construct a Probability Histogram:**

- Create a histogram to visually represent the probability distribution of $ x $. Each bar corresponds to a possible value of $ x $ on the horizontal axis, with the height representing the probability $ p(x) $.

This exercise will help illustrate concepts of probability distributions, specifically the binomial distribution, in a practical and engaging manner.

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