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 = 0.85.(a) use the normal approximation to find the probability that jodi scores 78% or lower on a 100-question test.(b) if the test contains 250 questions, what is the probability that jodi will score 78% or lower?

a) The probability that Jodi scores 78% or lower on a 100-question test is 4%.

b) The probability that Jodi scores 78% or lower on a 250-question test is 0.023%.

Step-by-step explanation:

a) To approximate this distribution we have to calculate the mean and the standard distribution.

The mean is the proportion p=0.85.

The standard deviation can be calculates as:

To calculate the probability that Jodi scores 78% or less on a 100-question test, we first calculate the z-value:

The probability for this value of z is

The probability that Jodi scores 78% or lower on a 100-question test is 4%.

b) In this case, the number of questions is 250, so the standard deviation needs to be calculated again:

To calculate the probability that Jodi scores 78% or less on a 250-question test, we first calculate the z-value:

The probability for this value of z is

The probability that Jodi scores 78% or lower on a 250-question test is 0.023%.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above