Question

The following table provides the daily charges, in dollars, for a sample of 15 hotels and motels operating in South Carolina. The data were found in the report South Campina Statistical Abstract, sponsored by the South Carolina Budget and Control Board.

a. Obtain a normal probability plot of the given data.

b. Use part $\left(a\right)$to identify any outliers.

c. Use part$\left(a\right)$to assess the normality of the variable under consideration.

Short answer

a. As a result, the normal probability plot for daily charges for hotels and motels shown above.

b. As a result, there are no outliers in the plot.

c. The daily charges are not approximately normally distributed.

Step-by-step solution

Part (a) Step 1: Given Information 

The normal probability of the given data.

Part (a) Step 2: Explanation 

The supplied data's normal probability,

If the probability distribution of a continuous random variable is described by the following, it is said to be regularly distributed or follows a normal probability distribution.

Arrange the given data in ascending order first, then use the table to calculate the normal scores.

Create a normal probability plot, as shown below.

As a result, the normal probability plot for daily charges for hotels and motels shown above.

Part (b) Step 3: Given Information 

The outliers in normal probability plot of part$a$.

Part (b) Step 4: Explanation 

Suspected values or outliers are the points at the line's upper or lower extremes, or those that are far away from it.

Outliers or uncommon values can be identified using probability values.

Take a look at part a's normal probability plot.

In the plot, there are no remarkable points.

As a result, there are no outliers in the plot.

Part (c) Step 5: Given Information 

The normality of the variable under consideration.

Part (c) Step 6: Explanation 

Consider portion a's normal probability plot.

The assumption of normalcy simply states that the underlying random variable of interest is distributed normally, or nearly so,

The information isn't transmitted in a straight path.

The variable under discussion isn't a straight line.

As a result, the daily charges are not allocated evenly.