Q:

A student takes a multiple choice test with 40 questions. The probability that a student answers a given question correctly is 0.5, independent of all other questions. The probability that the student answers more than N questions correctly is greater than 0.10. The probability that the student answers more than N+1 questions correctly is less than 0.10. Calculate N using normal approximation with continuity correction. Answer is 23. Please explain your work.

Accepted Solution

A:
Answer:Step-by-step explanation:X no of questions student answers is binomial with n =40 and p =0.5If approximated to normal, X is Normal withmean = np = 20 and variance = npq = 10P(X>N) >0.10We use std normal distribution table to get z value first then convert to x value[tex]z>-1.28[/tex]So [tex]x>20-1.28(10) = 20-12.8 = 7.2[/tex]This is with continuity correction.Hence without continuity correction this equals 7.2-0.5 = 6.7x>6.7n = 7