A history class has 75 members. If there is a 12% absentee rate per class meeting, find the mean, variance, and atandard deviation of the number of students who will be absent from each class

Variance is supposed to be 7.92

Mean = np = (75)(.12) = ?

Variance = npq = (75)(.12)(.88) = ?
(Note: q = 1 - p)

Standard deviation = square root of the variance

I'll let you finish the calculations.

for the standard deviation, I do not get that answer.

Mean=9

Variance=792
Standard Deviation=28.14

Well, history class can be a bit of a snooze sometimes, so I'm not surprised that there's an absentee rate. Let's crunch the numbers.

Given that the class has 75 members and there's a 12% absentee rate, we can calculate the expected number of absent students for each class meeting.

Mean = 75 * 0.12 = 9 students

To find the variance, we need to know the probability of each possible outcome. In this case, we only have two outcomes: students absent (9) and students present (75 - 9 = 66).

Variance = (9 * (1 - 9)²) + (66 * (0 - 66)²)
Variance = 5832 + 2592
Variance = 8424 students²

Finally, to calculate the standard deviation, we take the square root of the variance:

Standard deviation = √8424
Standard deviation ≈ 91.81 students

So, on average, you can expect around 9 students to be absent from each history class, with a variance of 8424 students² and a standard deviation of approximately 91.81 students. That's a lot of empty desks!

To find the mean, variance, and standard deviation of the number of students who will be absent from each class, you can follow these steps:

Step 1: Calculate the number of students who will be absent from each class meeting.

To find the number of students who will be absent, you need to calculate 12% of the class size. The formula for calculating a percentage is:
Percentage = (Number × Percentage) / 100

In this case, the class size is 75, and the percentage is 12, so the calculation would be:
Number of absentees = (75 × 12) / 100 = 9

So, there will be an average of 9 students absent from each class meeting.

Step 2: Calculate the variance.

The variance measures the spread of the data. To calculate the variance, use the formula:
Variance = (Sum of squares of differences from the mean) / (Number of data points)

Since the 12% absentee rate per class meeting remains constant, the number of absentees each time will be the same. Therefore, the variance will be zero.

Step 3: Calculate the standard deviation.

The standard deviation is the square root of the variance and provides a measure of how spread out the data is. As there is no variance in this case, the standard deviation will also be zero.

To summarize:
- Mean: 9 (average number of absent students per class meeting)
- Variance: 0 (no variance in the data)
- Standard deviation: 0 (no spread in the data)

In conclusion, the mean number of students who will be absent from each class meeting is 9, while both the variance and standard deviation are 0.