Question

In: Statistics and Probability

Using the information below, which is the eating out frequency of a single class of students....

Using the information below, which is the eating out frequency of a single class of students. Complete a write up that explains the normal, exponential, and lognormal distributions. Identify something unique and explain what value this adds. Consider a 30 day month and a 28 day month.

# of times eat out
1 4
2 18
3 12
4 5
5 5
6 11
7 17
8 7
9 4
10 15
11 0
12 16
13 6
14 1
15 12
16 12
17 10
18 16
19 5
20 16
21 3
22 3
23 10
24 20
25 5
26 0
27 4
28 10
29 6
30 0
31 30
32 20
33 0
34 12
35 14

Solutions

Expert Solution

Normal Distribution

The random variable X is said to follow normal distribution if:

  1. The probability distribution of X forms a symmetrical, bell shaped curve
  2. The mean, median and mode of X are equal
  3. The range of X is (-inf, inf)
  4. 68% of the results fall within one standard deviation and 95% fall within two standard deviations and 99% fall within three standard deviations from the mean of the distribution
  5. The parameters of the distribution are mean and standard deviation of X

Lognormal Distribution

The random variable X is said to follow lognormal distribution if:

  1. The log(X) follows normal distribution
  2. It is a positively skewed with longer right tail
  3. The range of X is (0 to inf)
  4. The parameters of the distribution are mean and standard deviation of X

Exponential Distribution

The random variable X is said to follow exponential distribution if:

  1. The range of X is from (0 to inf)
  2. The parameters of X is .
  3. The mean of the distribution is

Let the random variable X denote the number of times a class of students eat out. Let us see which distribution best suits the given data.

Based on the histogram we observe that the number of times a student eats out is positive and ranges from 0 to 30. Hence the number of times eat out does not follow normal distribution.

To check whether the distribution of the number of eat out follows exponential distribution, we tried to evaluate the memoryless property of exponential distribution.

The number of times a student eats out does not depend on the number of times he/she has eaten out in the past. Therefore the random variable X follows exponential distribution with mean 9.4(estimated from data) and rate parameter


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