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
.1587 will pass
so number of the 360 that will pass
= .1587(360)
= 57 rounded to the nearest person
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.
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.