FB: Attendance at a university's basketball games follows a Normal distribution with mean ì = 8,000 and standard deviation ó = 1,000. 60% of all games will have more than _______ people in attendance.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and its Z score. Insert the Z value into the equation above and solve for the score.
7750
To find the number of people in attendance for which 60% of all games will have more than that, we need to find the z-score corresponding to the given percentile (60%).
Step 1: Convert the given mean and standard deviation to a standard normal distribution (Z-distribution) by using the formula:
Z = (X - μ) / σ
Where:
Z = the z-score
X = number of people in attendance
μ = mean (8,000 in this case)
σ = standard deviation (1,000 in this case)
Step 2: Look up the z-score in the Z-table (or use a calculator) to find the corresponding percentile.
By looking up the z-score for a percentile of 60% in the Z-table, we can determine the value of Z. Let's calculate this.
Z = (X - μ) / σ
0.60 = (X - 8000) / 1000
Solving for X:
X - 8000 = 0.60 * 1000
X - 8000 = 600
X = 600 + 8000
X = 8600
Therefore, 60% of all games will have more than 8,600 people in attendance.