# Probability problem, central limit theorm/binomial

## 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?

## Answers and Replies

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The normal distribution table may give you numbers of P(Z < z), -inf to z. I think that you need to find P(.195 < Z < .4051), that would be P(Z < .4051) - P(Z < .195).