An average response rate for a marketing letter is 4% of the people who receive the letter respond to it. A company writes a new type of marketing letter, sends out 2,400 of them, and gets 65 responses. Explain whether the new type of letter would be considered to be a success.
65/2400 = 0.027 = 2.7%
To determine whether the new type of marketing letter is a success or not, let's compare the actual response rate with the average response rate.
Step 1: Calculate the average response rate:
The average response rate is given as 4%, so we can convert it to a decimal by dividing it by 100: 4/100 = 0.04.
Step 2: Calculate the expected number of responses:
To find the expected number of responses, we multiply the total number of letters sent (2,400) by the average response rate (0.04):
Expected responses = 2,400 * 0.04 = 96.
Step 3: Compare the actual responses to the expected responses:
- The company received 65 responses, which is less than the expected number of 96 responses.
Based on this comparison, we can conclude that the new marketing letter did not meet the average response rate and might not be considered a success.