A test has 200 points. THe mean is 120 and the standard deviation is 20. In order to pass the test one must score 140 points. If 360 people took the test how many passed
find the z-score for 140, then use your tables or charts or some software to find that
.1587 will pass
so number of the 360 that will pass
= .1587(360)
= 57 rounded to the nearest person
57
To find out how many people passed the test, we need to determine the cutoff score for passing based on the mean and standard deviation provided.
Step 1: Calculate the z-score for the cutoff score using the formula: z = (x - μ) / σ
Where:
x = cutoff score
μ = mean
σ = standard deviation
Given:
μ = 120
σ = 20
x = 140
Substituting the given values into the formula:
z = (140 - 120) / 20
z = 20 / 20
z = 1
Step 2: Use the z-score to find the proportion of scores that are below the cutoff using a standard normal distribution table or a calculator.
From the standard normal distribution table, we find that the proportion of scores below a z-score of 1 is approximately 0.8413.
Step 3: Multiply the proportion from step 2 by the total number of people who took the test to find the number of people who passed.
Number of people who passed = Proportion of scores below cutoff x Total number of test takers
Number of people who passed = 0.8413 x 360
Number of people who passed ≈ 302.88
Since we can't have a fraction of a person, we can round the result to the nearest whole number.
Approximately 303 people passed the test.
To find out how many people passed the test, you need to determine the number of test takers who scored above the passing score of 140 points.
First, let's calculate the Z-score for the passing score of 140 using the formula:
Z = (X - μ) / σ
Where:
X = passing score
μ = mean
σ = standard deviation
Plugging in the values:
Z = (140 - 120) / 20
Z = 20 / 20
Z = 1
Next, we need to find the area under the standard normal distribution curve to the right of this Z-score. This area represents the proportion of test takers who scored above the passing score.
Using a Z-table or a calculator, we can find that the area to the right of Z = 1 is approximately 0.1587.
Now, multiply this proportion by the total number of test takers:
Number of test takers who passed = 0.1587 * 360
Number of test takers who passed ≈ 57.37
Since we can't have fractional people, we round down the result to the nearest whole number.
Therefore, approximately 57 people passed the test.