Questions: What is the approximate percentage of buyers with paid search than 1,850? 65.4% What is the approximate percentage of buyers with paid between 1,500 and 1,850? 49.1% What is the approximate percentage of buyers with paid between 1,250 and 1,500? 36.8%

Solution Steps

Here's how to solve the first three questions related to the normal distribution of TV prices:

To work with the normal distribution, we convert prices to z-scores using the formula: z = (x - μ) / σ, where x is the price, μ is the mean ($1400), and σ is the standard deviation ($150).

• For $1850: z = (1850 - 1400) / 150 = 3
• For $1250: z = (1250 - 1400) / 150 = -1
• For $1550: z = (1550 - 1400) / 150 = 1

We use a z-table or calculator to find the area under the normal curve corresponding to these z-scores.

• Between $1400 and $1850 (z = 0 to z = 3): The area between z=0 and z=3 is 0.4987 (or 49.87%). Since the mean ($1400) corresponds to z=0, this area directly represents the percentage between $1400 and $1850.
• Between $1250 and $1550 (z = -1 and z = 1): The area between z=0 and z=1 is 0.3413, and due to symmetry it is the same area between z=0 and z = -1. Therefore the total area between z=-1 and z=1 is 2* 0.3413 = 0.6826 or 68.26%.
• More than $1850 (z > 3): Since the total area under the normal curve is 1 (or 100%), the area to the right of z=3 is 0.5 - 0.4987 = 0.0013, or 0.13%.

Final Answer