Astudent 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. explain your work.

Step-by-step explanation:

X no of questions student answers is binomial with n =40 and p =0.5

If approximated to normal, X is Normal with

mean = np = 20 and variance = npq = 10

P(X>N) >0.10

We use std normal distribution table to get z value first then convert to x value

So

This is with continuity correction.

Hence without continuity correction this equals 7.2-0.5 = 6.7

x>6.7

n = 7

step-by-step explanation:

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)