Question

The average score of 100 students taking a statistics test final with 70 with a standard deviation of seven. Assuming a normal distribution, approximately how many scored less than 60

Answer 1

Given that,

The average score of 100 students taking a statistics test final with 70 with a standard deviation of seven.

Assuming a normal distribution, approximately how many scored less than 60.

i.e,

n=100

Mean ()=70

Standard Deviation ()=7

P(X < 60):

Here, we use standard normal variate

z=-1.4286

Therefore,

=1−P ( Z<1.4286 )

[Since, from the z-score table]

=1−0.9236

=0.0764

Therefore, P(X < 60) =0.0764