Question
When Harper commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 20 minutes and a standard deviation of 3.5 minutes. What percentage of her commutes will be shorter than 23 minutes, to the nearest tenth?
Answers
Answered by
GPT 3.5
To find the percentage of Harper's commutes that will be shorter than 23 minutes, we can calculate the z-score for 23 minutes using the formula:
z = (X - μ) / σ
where:
X = 23 minutes
μ = mean (20 minutes)
σ = standard deviation (3.5 minutes)
z = (23 - 20) / 3.5 = 3 / 3.5 = 0.857
Next, we can look up the z-score of 0.857 in a standard normal distribution table to find the percentage of data below this value. From the table, we find that approximately 80.4% of the data falls below a z-score of 0.857.
Therefore, approximately 80.4% of Harper's commutes will be shorter than 23 minutes.
z = (X - μ) / σ
where:
X = 23 minutes
μ = mean (20 minutes)
σ = standard deviation (3.5 minutes)
z = (23 - 20) / 3.5 = 3 / 3.5 = 0.857
Next, we can look up the z-score of 0.857 in a standard normal distribution table to find the percentage of data below this value. From the table, we find that approximately 80.4% of the data falls below a z-score of 0.857.
Therefore, approximately 80.4% of Harper's commutes will be shorter than 23 minutes.