Question

A survey finds that the prices paid for six-year-old Tesla cars are normally distributed with a mean of $10,500 and a standard deviation of $500. Consider a sample of 1,000 people who bought six-year-old Teslas.

A) How many people paid between $10,000 and $11,000?

a) 341
b) 500
c) 682
d) 797

Answer 1

To calculate the number of people who paid between $10,000 and $11,000 for the six-year-old Tesla cars, we need to find the probability of a z-score between -1 and 1 using the standard normal distribution table.

This correct answer is c)

Step-by-step explanation:

To determine how many people paid between $10,000 and $11,000 for the six-year-old Tesla cars, we need to calculate the z-scores for both prices and use the standard normal distribution table.

The z-score formula is: z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.

For $10,000: z = (10000 - 10500) / 500 = -1

For $11,000: z = (11000 - 10500) / 500 = 1

Using the standard normal distribution table, we can find the probability associated with each z-score and subtract the lower probability from the higher probability.

The probability of a z-score between -1 and 1 is approximately 0.682. Therefore, 682 people paid between $10,000 and $11,000 for the six-year-old Tesla cars.

This correct answer is c)