A student is taking a true false test with 48 questions a Su

A student is taking a true false test with 48 questions. a) Suppose she has a probability p=3/4 of getting each question right. What is the probability that she will get at least 38 right? b) Answer the lsat question if she knows the answers to half of the question and flips a coin to answer the other half.

Note: Solution should come from the Normal Approximation (Central Limit Theorem)

Solution

a)

We first get the z score for the critical value:          
          
x = critical value =    37.5      
u = mean = np =    36      
          
s = standard deviation = sqrt(np(1-p)) =    3      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.5      
          
Thus, the left tailed area is          
          
P(z >   0.5   ) =    0.308537539 [ANSWER]

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b)

She has 24 correct already then. Thus, she needs at least 14 more.

We first get the z score for the critical value:          
          
x = critical value =    13.5      
u = mean = np =    12      
          
s = standard deviation = sqrt(np(1-p)) =    2.449489743      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.612372436      
          
Thus, the left tailed area is          
          
P(z >   0.612372436   ) =    0.270145687 [ANSWER]