In: Statistics and Probability
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 |
Normal Distribution
The random variable X is said to follow normal distribution if:
Lognormal Distribution
The random variable X is said to follow lognormal distribution if:
Exponential Distribution
The random variable X is said to follow exponential distribution if:
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