For 7, To find the percentage of test takers that scored lower than Lorena, we need to find the area under the normal distribution curve to the left of her score of 554.
Using the standard normal distribution table, we can find the z-score corresponding to Lorena's score:
z = (x - μ) / σ = (554 - 495) / 20 = 2.95
Looking up the z-score of 2.95 in the standard normal distribution table, we find that the area to the left of this z-score is 0.9985.
Therefore, Lorena scored better than approximately 99.9% of the test takers, which we round to one decimal place as 99.9%.
On the 8th question, Given that the prices of bicycles are normally distributed with a mean (μ) of $208 and a standard deviation (σ) of $8, we need to find the percentage of bicycles priced greater than $203.
First, we need to calculate the z-score using the formula:
z = (X - μ) / σ
where X is the value we want to find the percentage for.
z = (203 - 208) / 8 = -0.625
Using a standard normal distribution table or calculator, we can find that the percentage of bicycles priced greater than $203 is 73.4% (rounded to one decimal place).
Therefore, approximately 73.4% of bicycles are priced greater than $203.