The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $2000 and the standard deviation is $65.
What is the approximate percentage of buyers who paid between $1805 and $2000?
To find the approximate percentage of buyers who paid between $1805 and $2000, we need to calculate the z-scores for these two values using the formula:
z = (X - μ) / σ
For $1805:
z1 = (1805 - 2000) / 65
= -195 / 65
≈ -3
For $2000:
z2 = (2000 - 2000) / 65
= 0 / 65
= 0
Next, we need to find the corresponding probabilities of these z-scores from the standard normal distribution table. A z-score of -3 has an approximate probability of 0.0013, and a z-score of 0 has a probability of 0.5000.
To find the percentage of buyers who paid between $1805 and $2000, we subtract the probability of the lower z-score from the probability of the higher z-score:
Probability between $1805 and $2000 = 0.5000 - 0.0013
= 0.4987
Finally, we convert this probability to a percentage by multiplying by 100:
Percentage between $1805 and $2000 ≈ 0.4987 x 100
≈ 49.87%
Approximately, 49.87% of buyers paid between $1805 and $2000 for the HD television.