2. The manager of a sandwich shop gathers data on what people spend on lunch on a particular day of the week.
The results are $4.20, $4.22, $2.35, $4.32, $5.25, $6.48, $6.78, $8.59, $6.95, $5.52, $6.83, $7.35, $4.36, $9.39, $6.42.
To the degree that this represents the population of all those who eat lunch at sandwich shops, what percentage of customers spend:
1. less than $4.34?
2. between $3.50 and $4.80?
3. less than $2.35?
Imagine that you are the manager of a sandwich shop. Based on your calculations, what do you think is the best pricing point for your shop? What would you do to increase sales at the sandwich shop?
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.
I'll let you do the calculations and come to your own conclusions.
To answer these questions, we need to calculate the percentages based on the data provided. Here's the step-by-step process to find the answers:
1. To calculate the percentage of customers who spend less than $4.34, we count the number of customers whose spending is less than $4.34 and divide it by the total number of customers.
In the given data set, the customers who spend less than $4.34 are: $4.20, $4.22, $2.35, $4.32, $4.36
Counting the number of customers, we have 5 customers who spend less than $4.34.
To find the percentage, we divide 5 by the total number of customers in the dataset and multiply by 100:
Percentage of customers who spend less than $4.34 = (5 / 15) * 100 = 33.33%
Therefore, approximately 33.33% of customers spend less than $4.34.
2. To calculate the percentage of customers who spend between $3.50 and $4.80, we count the number of customers whose spending falls within this range and divide it by the total number of customers.
In the given data set, the customers who spend between $3.50 and $4.80 are: $4.20, $4.22, $4.32, $4.36
Counting the number of customers, we have 4 customers who spend between $3.50 and $4.80.
To find the percentage, we divide 4 by the total number of customers in the dataset and multiply by 100:
Percentage of customers who spend between $3.50 and $4.80 = (4 / 15) * 100 = 26.67%
Therefore, approximately 26.67% of customers spend between $3.50 and $4.80.
3. To calculate the percentage of customers who spend less than $2.35, we count the number of customers whose spending is less than $2.35 and divide it by the total number of customers.
In the given data set, the customers who spend less than $2.35 are: $2.35
Counting the number of customers, we have 1 customer who spends less than $2.35.
To find the percentage, we divide 1 by the total number of customers in the dataset and multiply by 100:
Percentage of customers who spend less than $2.35 = (1 / 15) * 100 = 6.67%
Therefore, approximately 6.67% of customers spend less than $2.35.
Based on these calculations, the manager can analyze the pricing point for the shop and make a decision. As the data represents the population of all those who eat lunch at sandwich shops, it can provide insights into customer behavior.
To increase sales at the sandwich shop, the manager can consider the following strategies:
1. Customer surveys: Conducting surveys to understand customer preferences and expectations can provide valuable insights. This can help the manager tailor the menu and pricing to better meet customer needs.
2. Special offers and promotions: Introducing weekly specials, discounts, and loyalty programs can attract new customers and incentivize repeat visits.
3. Expanding menu options: Offering a diverse range of sandwiches, sides, and drinks can cater to different customer preferences and increase the chances of attracting a wider customer base.
4. Improving customer experience: Focusing on excellent customer service, cleanliness, and ambiance can enhance the overall experience, encouraging customers to return and recommend the shop to others.
5. Marketing and advertising: Promoting the sandwich shop through targeted marketing campaigns, social media presence, and partnerships with local businesses can help increase its visibility and attract new customers.
By combining these strategies and analyzing the data trends, the manager can make informed decisions to optimize pricing and increase sales at the sandwich shop.