Question

Suppose an exam consisted of 10 multiple choice problems, each with five possible responses (A-E), only 1 of which is correct. If a student randomly guesses the answers to each question then what is the probability that a student guesses the correct answer to exactly 7 questions? Additionally, what is the probability that a student passes the exam with a score of 70% or higher? (round to 5 decimal places).

Please explain using the TI84 Calculator (I currently own Plus CE) and via formula for better understanding.

Answer 1

here this is binomial distribution with parameter p=1/5 and n=10

1) probability that a student guesses the correct answer to exactly 7 questions =P(X=7)=0.00079

(for TI84 Calculator press 2nd-vars -binompdf -trails :10 ; p value :0.2 ; x : 7)

2)

probability that a student passes the exam with a score of 70% or higher =P(X>=7)=1-P(X<=6)=1-0.99914=0.00086

((for TI84 Calculator press 2nd-vars -binomcdf -trails :10 ; p value :0.2 ; x : 6   and then deduct 1 from result value)