There are n questions on a multiple choice exam, and for each question, there are four choices. To pass the exam, one must correctly answer at least 70% of the questions. The student has not studied, so he/she has to resort to guessing on every question.
a. Find the probability of the student passing for n = 10.b. Find the expected number of questions answered correctly for n = 20.c. Find the variance for the number of questions answered correctly for n = 10.

a) 0.352% probability of the student passing

b) 5

c) 1.875

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student answers it correctly, or he answers it wrong. The probability of correctly answering a question is independent from the probability of correctly answering other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is:

The variance of the binomial distribution is:

For each question, there are four choices.

One choice is correct, so

a. Find the probability of the student passing for n = 10.

0.7*10 = 7

This is when

0.352% probability of the student passing

b. Find the expected number of questions answered correctly for n = 20.

Here we have n = 20. So

c. Find the variance for the number of questions answered correctly for n = 10.

Here we have n = 10.

it would take 7/10 of an hour too fill the pool.

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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