A student takes a multiple-choice test that has nine questions. Each question has four choices. The student guesses randomly at each question. Let X be The number of questions answered correctly. Round the answer at least four decimal places. a) Find P(3) b) Find P(more than 1)

y/x=18

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.

1332.

this is because to get from 333 to 999 you multiply by 3, and you should do the same to the number of hours.

therefore you would do 444*3=1332