Question

Approximately 54% of mathematics students do their homework on time. In a class of 250 students, what is the mean, variance, and standard deviation if we assume normality and use the normal distribution as an approximation of the binomial distribution?

A) Mean = 135 Variance = 62 Standard Deviation = 8B) Mean = 53 Variance = 62 Standard Deviation = 8C) Mean = 54 Variance = 8 Standard Deviation = 62D) Mean = 135 Variance = 8 Standard Deviation = 62

Answer 1

A) Mean = 135 Variance = 62 Standard Deviation = 8

Explanation:

Given that :

Proportion (p) = 54%

Sample size (n) = 250

Using Normal approximation :

Mean = np

Mean = 250 * 0.54 = 135

Variance = npq ; q = 1 - p = 1 - 0.54 = 0.46

Variance = (250 * 0.54 * 0.46) = 62.1 = 62

Standard deviation = √variance = √62.1

Standard deviation = 7.8803553 = 8