The amount of protein (in grams) for a variety of fast-food sandwiches is reported here.

```
23 30 20 27 44 26 35 20 20 29
25 15 18 27 19 22 12 26 34 15
27 35 26 43 35 14 24 12 23 31
40 35 38 57 22 42 24 21 27 33
```

a. Find the amount of protein in the 4th percentile.

b. What is the percentile of a sandwich with 38 grams of protein?

c. Construct a stem plot.

d. How many fast-food sandwiches contain less than 26 grams of protein?

e. Find the proportion of sandwiches with less than 18 grams of proteins.

f. Find the proportion of sandwiches with 27 OR 35 grams of protein.

#### Solution

```
protein<-c(23, 30, 20, 27, 44, 26, 35, 20, 20,
29, 25, 15, 18, 27, 19, 22, 12, 26, 34, 15, 27,
35, 26, 43, 35, 14, 24, 12, 23, 31, 40, 35, 38,
57, 22, 42, 24, 21, 27, 33)
```

a. To find the 4th percentile we use `quantile()`

function

`quantile(protein,c(0.04))`

```
4%
13.12
```

The amount of protein in the 4th percentile 13.12.

b. percentile of a sandwich with 38 grams of protein

```
most38<-protein[protein<=38]
most38
```

```
[1] 23 30 20 27 26 35 20 20 29 25 15 18 27 19 22 12 26 34 15 27 35 26 35 14 24
[26] 12 23 31 35 38 22 24 21 27 33
```

```
prop38<-length(most38)/length(protein)
prop38
```

`[1] 0.875`

Percentile of a sandwich with 38 grams of protein is 0.875.

c. Stem plot of amount of protein

`stem(protein)`

```
The decimal point is 1 digit(s) to the right of the |
1 | 224
1 | 5589
2 | 0001223344
2 | 566677779
3 | 0134
3 | 55558
4 | 0234
4 |
5 |
5 | 7
```

d. Fast-food sandwiches that contain less than 26 grams of protein

```
prop26<-protein[protein<26]
length(prop26)
```

`[1] 18`

Fast-food sandwiches that contain less than 26 grams of protein are 18

e. The proportion of sandwiches with less than 18 grams of proteins.

```
prot18<-protein[protein < 18]
prot18
```

`[1] 15 12 15 14 12`

```
prop18<-length(prot18)/length(protein)
prop18
```

`[1] 0.125`

The proportion of sandwiches with less than 18 grams of proteins is 0.125.

f. Find the proportion of sandwiches with 27 OR 35 grams of protein.

```
prot27or35<-protein[protein == 27 | protein ==35 ]
prot27or35
```

`[1] 27 35 27 27 35 35 35 27`

```
prop27or35<-length(prot27or35)/length(protein)
prop27or35
```

`[1] 0.2`

The proportion of sandwiches with 27 OR 35 grams of protein = 0.2.

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators