In a maths class the bottom 16% of student are given an F grade. If the class mean is 63 and standard deviation is 18, what score must a student get to pass?
well, what value z corresponds to
P(Z>z) = .84?
To find the score required to pass, we need to determine the cutoff point below which the bottom 16% of students fall.
Step 1: Find the Z-score
The Z-score can be calculated using the formula:
Z = (X - μ) / σ
Where:
X = The raw score
μ = The mean
σ = The standard deviation
Step 2: Find the corresponding percentile
Since we want to find the score below which 16% of the students fall, we need to find the Z-score that corresponds to the 16th percentile.
Step 3: Use Z-score to find the score
Using the Z-score we calculated in Step 2, we can find the corresponding score by rearranging the Z-score formula:
X = Z * σ + μ
Now let's calculate the required score step by step.
Step 1: Find the Z-Score
To find the Z-score corresponding to the 16th percentile, we need to find the Z-value using a standard normal distribution table or a calculator. The Z-value for the 16th percentile is approximately -1.04.
Step 2: Convert Z-Score to Score
Now we can use the Z-value to find the score using the formula:
X = Z * σ + μ
X = (-1.04) * 18 + 63
X ≈ 44.72
Therefore, a student must score approximately 44.72 to pass the class.