Question

Exams have a mean of 73 and a standard deviation of 7.8. If 24 students are randomly selected, find P(X>78).

I was able to solve this problem but I need an explanation as to why we have to use "z = (78-73) / (7.8/sqrt24)" instead of just using "z = (78-83) / 7.8)". How do I differentiate between the two? In other words, when do I have to divide the standard deviation by the square root of sample size n?

Answer 1

Solution :

Given that ,

mean = = 73

standard deviation = = 7.8

n = 24

= 73 and

= / n = 7.8 / 24 = 1.5922

P(? > 78) = 1 - P( < 78) = 1 - P(( - ) / < (78 - 73) / 1.5922) = 1 - P(z < 3.14)

    Using standard normal table,

P( > 78) = 1 - 0.9992 = 0.0008

Probability = 0.0008