BioStats Sampling Distribution help? My teacher has yet to go over this in class

Question

BioStats Sampling Distribution help?

My teacher has yet to go over this in class, and this is due tonight. Really anything insights would be greatly appreciated as I don't even know where to start and what equations that I should be using. Thank you in advance!

(1)

(2)

(3)

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent, Jodi is a good student for whom p = 0.78 (a) Use the normal approximation to find the probability that Jodi scores 72% or lower on a 100-question test. (Round your answer to four decimal places.) (b) If the test contains 250 questions, what is the probability that Jodi will score 72% or lower? (Use the normal approximation. Round your answer to four decimal places.) (c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test? questions

Explanation / Answer

1.

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.72      
u = mean = p =    0.78      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.04142463      
          
Thus,          
          
z = (x - u) / s =    -1.448413649      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.448413649   ) =    0.0737507 [ANSWER]

****************

b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.72      
u = mean = p =    0.78      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.026199237      
          
Thus,          
          
z = (x - u) / s =    -2.290143062      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.290143062   ) =    0.011006512 [ANSWER]

********************

c)

As the standard deviation of proportion varies inversely as the square root of the proportion, then we need a sample size 4 times the original.

Hence,

n = 4*100 = 400. [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.