The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. (Z=(x-u)/standard deviation
If students are given 85 min to complete the exam what Probability that students will not finish?
What percent of students will complete the exam between 63 min and 80 min?
You can play around with Z table stuff here:
http://davidmlane.com/hyperstat/z_table.html
To find the probability that students will not finish the exam within the given time limit of 85 minutes, we need to find the area under the normal distribution curve to the right of 85 minutes.
Step 1: Standardize the value of 85 minutes using the formula Z = (x - μ) / σ, where x = 85, μ = 70, and σ = 10.
Z = (85 - 70) / 10
Z = 1.5
Step 2: Find the probability of Z > 1.5. This can be done by looking up the corresponding area in the Z-table or using a calculator with a normal distribution function. Let's assume the probability is P(Z > 1.5) = 0.0668 (rounded to four decimal places).
Therefore, the probability that students will not finish the exam within 85 minutes is approximately 0.0668 or 6.68%.
Now, let's move on to the second question.
To find the percent of students who will complete the exam between 63 minutes and 80 minutes, we need to find the area under the normal distribution curve between these two values.
Step 1: Standardize the values of 63 minutes and 80 minutes using the formula Z = (x - μ) / σ, where x1 = 63, x2 = 80, μ = 70, and σ = 10.
For 63 minutes:
Z1 = (63 - 70) / 10
Z1 = -0.7
For 80 minutes:
Z2 = (80 - 70) / 10
Z2 = 1
Step 2: Find the probability of Z1 < Z < Z2. This can also be done by looking up the corresponding areas in the Z-table or using a calculator with a normal distribution function. Let's assume the probability is P(-0.7 < Z < 1) = 0.4082 (rounded to four decimal places).
Therefore, approximately 40.82% of students will complete the exam between 63 minutes and 80 minutes.
To find the probability that students will not finish the exam within the given time of 85 minutes, we need to find the area under the normal curve to the right of 85 minutes.
First, we need to calculate the z-score for the given time of 85 minutes using the formula: Z = (x - μ) / σ, where x is the given time, μ is the mean, and σ is the standard deviation.
Z = (85 - 70) / 10
Z = 15 / 10
Z = 1.5
Next, we need to find the area under the normal curve to the right of the calculated z-score of 1.5. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table, we find that the area to the right of 1.5 is approximately 0.0668. This represents the probability that a student will not finish the exam within the given time.
So, the probability that students will not finish the exam within 85 minutes is approximately 0.0668 or 6.68%.
Now, let's calculate the percentage of students who will complete the exam between 63 minutes and 80 minutes.
First, we need to calculate the z-scores for the given times of 63 minutes and 80 minutes.
For 63 minutes:
Z = (63 - 70) / 10
Z = -7 / 10
Z = -0.7
For 80 minutes:
Z = (80 - 70) / 10
Z = 10 / 10
Z = 1
Next, we need to find the area under the normal curve between the calculated z-scores of -0.7 and 1. This represents the percentage of students who will complete the exam between 63 minutes and 80 minutes.
Using a standard normal distribution table, we find that the area between -0.7 and 1 is approximately 0.3797.
Now, we can calculate the percentage as a decimal by multiplying this area by 100.
Percentage = 0.3797 * 100
Percentage = 37.97%
Therefore, approximately 37.97% of students will complete the exam between 63 minutes and 80 minutes.