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## Homework Statement

if a student writes a true-false test and guesses each answer, what is the probability that he can get 120 to 140 correct answers if there are 200 questions on the test?

## Homework Equations

central limit theorm and binomial distribution

my teacher game me a chart that gives area under a normal curve for given z-values ranging from 3.4 to -3.4

## The Attempt at a Solution

what i have so far is: n= 200 np(mean)= (0.5)(200)= 100 standard deviation= sqrt(0.5)(0.5)(200)= 7.07

since the question wants the probability between 120 and 140 (im guessing this is inclusive, the question doesnt specify) i have:

P(120<=x<=140)

= P(119.5<x<140.5)

= 119.5-100/7.07(sqrt200)<x<140.5-100/7.07(sqrt200)

after the calculation i get:

0.1950<z<0.4051

now, i know i go to my table and get the areas under the curves for those two numbers, but what do i do next dince i have the two numbers? do i subtract them?