Question

(1 point) Suppose the scores of students on a Statistics course are Normally distributed with a mean of 226 and a standard deviation of 67.
What percentage of the students scored between 226 and 360 on the exam? (Give your answer to 3 significant figures.)
percent.

(1 point) Suppose the scores of students on an test are Normally distributed with a mean of 186 and a standard deviation of 42. Then approximately 99.7% of the test scores lie between the numbers  and   such that the mean is halfway between these two integers.

Answer 1

Ans1:

#Given:

=226

=67

#X=scores of students on a Statistics course

x~N(226,67)

What percentage of the students scored between 226 and 360 on the?

ie P(226<x<360)=P((226-226)/67)<(x-)/<(360-226)/67)

=P(0<z<2)

=P(z<2)-P(z<0)

=0.9773-0.5

=0.4773

# 47.7%  of the students scored between 226 and 360

Ans2:

Approximately 99.7% area lies within 3 standard deviations

Lower score = mean - 3 * sd = 186 - 3 * 42= 60

Upper score = mean + 3 * sd = 186 + 3 * 42 = 312

approximately 99.7% of the scores lie between the numbers 60 and 312