# Math Help - Probability + normal distribution

1. ## Probability + normal distribution

so my take-home quiz consists of a problem that i haven't been able to figure out, and i met similar frustration from my classmates as well.

we are studying normal distribution as of now, and what seems a binomial problem this is a hard nut to crack:

" a multiple choice test consists of 60 questions. each question has 4 possible answers of which one is correct. if all answers are random guesses, estimate the probability of getting at least 20% correct. "

also, the instructions indicate to find the probability using the normal distribution as an approximation to the binomial distribution.

my guesses are as follows:

1. find z-score and use table, but i think it's out of the question to calculate standard deviation in this case

2. use normalpdf or binomial pdf using TI-83 (n=60, p=.25) but really, have no idea where to go from there

3. make a chart of x and P(x), or all outcomes on my TI-83 with binomial values and calculate standard deviation.

please lead me in the right direction. i don't really need the answer, i just need to figure out how to get it!

2. Originally Posted by hopespaul
so my take-home quiz consists of a problem that i haven't been able to figure out, and i met similar frustration from my classmates as well.

we are studying normal distribution as of now, and what seems a binomial problem this is a hard nut to crack:

" a multiple choice test consists of 60 questions. each question has 4 possible answers of which one is correct. if all answers are random guesses, estimate the probability of getting at least 20% correct. "

also, the instructions indicate to find the probability using the normal distribution as an approximation to the binomial distribution.

my guesses are as follows:

1. find z-score and use table, but i think it's out of the question to calculate standard deviation in this case

2. use normalpdf or binomial pdf using TI-83 (n=60, p=.25) but really, have no idea where to go from there

3. make a chart of x and P(x), or all outcomes on my TI-83 with binomial values and calculate standard deviation.

please lead me in the right direction. i don't really need the answer, i just need to figure out how to get it!

Are you familiar with the normal approximation to the binomial distribution? If so, where do you get stuck using it? If not, read this: Binomial distribution - Wikipedia, the free encyclopedia (5.2) and then state where you're stuck if you still are.

3. i know some about it, but i'm not exactly sure how to calculate the z-score of the 20th percentile

4. Originally Posted by hopespaul
i know some about it, but i'm not exactly sure how to calculate the z-score of the 20th percentile
Find the value of z* such that Pr(Z < z*) = 0.2.