Use the following information to answer questions 2 and 3 Th

Use the following information to answer questions 2 and 3.

The registrar of a large university knows that 30% of the students come to college with credit for an advance placement (AP) course. The registrar is going to conduct interviews with students regarding their experiences at the university. Depending on which students are chosen, the proportion of students in the sample that have AP credit may vary.

Question 2

In a sample of 100 students, what is the probability that over 35% of the sample has AP credit?

Give your answer to 4 decimal places. For help on how to input a numeric answer, please see \"Instructions for inputting a numeric response.\"

Question 3

In a sample of 200 students, what is the probability that over 33% of the sample has AP credit?

Give your answer to 4 decimal places. For help on how to input a numeric answer, please see \"Instructions for inputting a numeric response.\"

Solution

2.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.35      
u = mean = p =    0.3      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.045825757      
          
Thus,          
          
z = (x - u) / s =    1.091089451      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.091089451   ) =    0.1376 [ANSWER]

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3.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.33      
u = mean = p =    0.3      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.032403703      
          
Thus,          
          
z = (x - u) / s =    0.9258201      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.9258201   ) =    0.1773 [ANSWER]