ALICE and YouGov conducted an online poll among Americans hotel guests of more than 18 years old to understand their expectations from hotels in the year 2018-191. This poll showed that 40% of guests were interested in gaining experiences of local cuisine tastings/tours. Suppose you take a random sample of 15 hotel guests.Let, x, represent the number of guests interested in gaining experiences of local cuisine tastings/tours.Find the mean and standard deviation of x.What is the probability that x <=10?Find the probability that x > 12.Find the probability that x = 11. **Binomial Distribution Calculation**| Description | Symbol | Value ||------------------------------------------------|--------|-------|| Number of trials | n | 4 || Number of successes | x | 4 || Probability of success in a single trial | p | 0.66 || Probability of failure | q | 0.34 || **Probability** | | 0.190 || **Mean** | | 2.64 || **Variance** | | 0.90 || **Standard Deviation** | | 0.95 |This table provides the calculation details for a binomial distribution:- **Number of trials (n):** The total number of experiments conducted, which is 4.- **Number of successes (x):** The count of desired outcomes, also 4.- **Probability of success in a single trial (p):** Set at 0.66.- **Probability of failure (q):** Calculated as 1 - p, which is 0.34.Key values calculated from the binomial distribution include:- **Probability:** The likelihood of achieving exactly 4 successes in 4 trials is 0.190.- **Mean:** The average expected successes in the trials is 2.64.- **Variance:** The measure of the spread is 0.90.- **Standard Deviation:** The square root of the variance, indicating dispersion, is 0.95.

Answered: Let, x, represent the number of guests…

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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ALICE and YouGov conducted an online poll among Americans hotel guests of more than 18 years old to understand their expectations from hotels in the year 2018-19¹. This poll showed that 40% of guests were interested in gaining experiences of local cuisine tastings/tours. Suppose you take a random sample of 15 hotel guests.

Let, x, represent the number of guests interested in gaining experiences of local cuisine tastings/tours.

Find the mean and standard deviation of x.
What is the probability that x <=10?
Find the probability that x > 12.
Find the probability that x = 11.

**Binomial Distribution Calculation**

| Description | Symbol | Value |
|------------------------------------------------|--------|-------|
| Number of trials | n | 4 |
| Number of successes | x | 4 |
| Probability of success in a single trial | p | 0.66 |
| Probability of failure | q | 0.34 |
| **Probability** | | 0.190 |
| **Mean** | | 2.64 |
| **Variance** | | 0.90 |
| **Standard Deviation** | | 0.95 |

This table provides the calculation details for a binomial distribution:

- **Number of trials (n):** The total number of experiments conducted, which is 4.
- **Number of successes (x):** The count of desired outcomes, also 4.
- **Probability of success in a single trial (p):** Set at 0.66.
- **Probability of failure (q):** Calculated as 1 - p, which is 0.34.

Key values calculated from the binomial distribution include:

- **Probability:** The likelihood of achieving exactly 4 successes in 4 trials is 0.190.
- **Mean:** The average expected successes in the trials is 2.64.
- **Variance:** The measure of the spread is 0.90.
- **Standard Deviation:** The square root of the variance, indicating dispersion, is 0.95.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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