Suppose that the average weight of students in a statistics class is 75.5 kilograms with a standard deviation of 10.3 kilograms.
B. What percent of students have weights greater than 80.1 kilograms?
Use z-scores:
z = (x - mean)/sd
With your data:
z = (80.1 - 75.5)/(10.3) = ?
I'll let you finish the calculation.
Once you have the z-score, check a z-table for the probability. Remember the problem is asking what percent of students have weights "greater than" 80.1 kilograms. Keep that in mind when looking at the table. Also remember to convert to a percent.
I hope this will help get you started.
Thank you that helps a lot. I have been struggling with this.
C. What percent of students weigh less than 60.1 kilograms?
Z=(60.1-75.5)/10.3=-1.49
I checked the z-table and the probability is .0681.
.0681*100=6.8%
Is this problem correct?
Yes
Yes! Thanks. :)
I have one more question.
Suppose that the average weight of students in a statistics class is 75.5 kilograms with a standard deviation of 10.3 kilograms.
Using the 68-95-99.7 rule, what is the lower bound for the weight of the top 2.5% of students.
To find the percentage of students with weights greater than 80.1 kilograms, we will first need to determine the z-score corresponding to this weight.
The z-score measures how many standard deviations an individual data point is from the mean. It can be calculated using the formula:
z = (X - μ) / σ
Where:
X = individual data point (weight)
μ = mean (average weight)
σ = standard deviation
In this case, X = 80.1 kg, μ = 75.5 kg, and σ = 10.3 kg.
Calculating the z-score:
z = (80.1 - 75.5) / 10.3
z = 4.6 / 10.3
z ≈ 0.447
Once we have the z-score, we can then find the percentage using a standard normal distribution table or a statistical calculator.
Looking up the z-score of 0.447 in a standard normal distribution table, we find that the corresponding percentage is approximately 67.69%.
Therefore, approximately 67.69% of students have weights greater than 80.1 kilograms.