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%.

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.