It is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 1616 students in the class, what is the probability that the first 22 presentations will be by Drake and Todd, in that order

= 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, since the order in which the students are chosen is important, the permutations formula is used to solve it.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

Desired outcomes:

Drake then Todd, so only one outcome, which means that

Total outcomes:

Two students from a set of 16, so:

What is the probability that the first 2 presentations will be by Drake and Todd, in that order?

= 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.

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.

answer: 1.06 km per sec

step-by-step explanation:

39.6 m=63.72 km

60 min in an hour so 63.72/60=1.06