In a city in the Southwest, restaurants charge on the average $15.65 for a steak dinner (with a standard deviation of $0.65), $8.65 for a chicken dinner (with a standard deviation of $0.35), and $22.95 for a lobster dinner (with a standard deviation of $1.30).
If a restaurant in this city charges $16.25 for a steak dinner, $9.15 for a chicken dinner, and $23.95 for a lobster dinner, which of the three dinners is relatively more overpriced?

The chicken dinner is relatively more overpriced because of its highest standard score value

Step-by-step explanation:

In this question, we have three dinners, we now need to know the which of the three dinners is relatively overpriced than the others given the data in the question.

We proceed as follows;

To calculate how relatively one of the dinner compares to another, we use the z-score of each of the dinners. The z-score is otherwise referred to as standard score and what it gives us is how far the value we have is from the mean( average)

Mathematically z score can be calculated as follows;

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation and x is the value given.

We calculate for each of the dinners and then draw a conclusion based on which has the lowest z score value to indicate the relative cheapness

The restaurants charge on the average $15.65 for a steak dinner, with a standard deviation of $0.65.

A particular restaurant in this city charges $16.25 for a steak dinner.

Now, we know that the relative price is measured by the ratio of the difference between the observation and the mean, to the standard deviation.

So, the relative price for steak dinner in the restaurant is

=(16.25-15.65)/0.65

=0.60/0.65

=0.9230.

The restaurants charge on the average $8.65 for a chicken dinner, with a standard deviation of $0.35.

The particular restaurant in this city charges $9.15 for a chicken dinner.

Now, we know that the relative price is measured by the ratio of the difference between the observation and the mean, to the standard deviation.

So, the relative price for chicken dinner in the restaurant is

=(9.15-8.65)/0.35

=0.50/0.35

=1.4285.

The restaurants charge on the average $22.95 for a lobster dinner, with a standard deviation of $1.30.

A particular restaurant in this city charges $23.95 for a lobster dinner.

Now, we know that the relative price is measured by the ratio of the difference between the observation and the mean, to the standard deviation.

So, the relative price for lobster dinner in the restaurant is

=(23.95-22.95)/1.30

=1/1.30

=0.7692.

So, here we see that the realtive price of chicken dinner is $1.4285, which is greater than the relative price for steak and lobster dinner.

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