probability: binomial probability

soleinovell

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Hi, I've exhausted every method I know to try and answer this so hopefully someone here can help me.. I need to know what the probability that a student chosen at random out of 100 students will have a reaction time of less than 0.2 seconds.. the mean is 0.2528 and the standard deviation is 0.0412.
I know that I need to find the Z score (which was -1.282) however, I have no idea how to draw the diagrams (bell shape curve) and to find the actual probability of it..

My second question is how do I use binomial probability distribution (Bernoulli trial) to determine out of 20 of the people, what is the probability of one student having a reaction time less than 0.2?

If someone can help me ill be most grateful
 
Hi, I've exhausted every method I know to try and answer this so hopefully someone here can help me.. I need to know what the probability that a student chosen at random out of 100 students will have a reaction time of less than 0.2 seconds.. the mean is 0.2528 and the standard deviation is 0.0412.
I know that I need to find the Z score (which was -1.282) however, I have no idea how to draw the diagrams (bell shape curve) and to find the actual probability of it..

My second question is how do I use binomial probability distribution (Bernoulli trial) to determine out of 20 of the people, what is the probability of one student having a reaction time less than 0.2?

If someone can help me ill be most grateful

You need to estimate the integral or use a table of values to find the closest z-score to it in the table and its associated probability.

For your second question, it depends on if your question means "at least one student" or "exactly one student." Say the probability for the above question is \(\displaystyle p\). Then Probability(at least one) = 1-Probability(none). And the probability of no students having a reaction time of less than .2 s is \(\displaystyle {20\choose 0} p^0(1-p)^{20}\)
 
You need to estimate the integral or use a table of values to find the closest z-score to it in the table and its associated probability.

For your second question, it depends on if your question means "at least one student" or "exactly one student." Say the probability for the above question is \(\displaystyle p\). Then Probability(at least one) = 1-Probability(none). And the probability of no students having a reaction time of less than .2 s is \(\displaystyle {20\choose 0} p^0(1-p)^{20}\)

Pardon my ignorance, but what is an integral?

Sorry, the second question was the probability of at least one student .. im confused as to what p and q would equal?
 
Pardon my ignorance, but what is an integral?

Sorry, the second question was the probability of at least one student .. im confused as to what p and q would equal?

You should have a table to look up z-scores to find the probability (p). And q is always 1-p. Don't worry about that I said about an integral.
 
Hi, I've exhausted every method I know to try and answer this so hopefully someone here can help me.. I need to know what the probability that a student chosen at random out of 100 students will have a reaction time of less than 0.2 seconds.. the mean is 0.2528 and the standard deviation is 0.0412.
I know that I need to find the Z score (which was -1.282) however, I have no idea how to draw the diagrams (bell shape curve) and to find the actual probability of it..

My second question is how do I use binomial probability distribution (Bernoulli trial) to determine out of 20 of the people, what is the probability of one student having a reaction time less than 0.2?

If someone can help me ill be most grateful
A wonderful feature of the normal distribution is that the curve always is the same .. only the horizontal scale changes. The peak of the curve is the mean, 0.2528 s. Estimate where the curve falls to 60% of its peak value (e^{-1/2} to be exact). The width of the curve at that height is from -1 to +1 standard deviations.

From the table of the normal distribution, for a z-score of -1.282 the probability of being further than that from the mean is 0.100. Call that p for use in the binomial distribution. That is, "The probability of a single measurement being less than 0.2s is p = 0.100." Then the probability of >0.2s is q = 1-p = 0.900.

The probability of at least one student is P(>0) = 1 - P(0). That is, calculate probability that all 20 are >0.2s, and subtract that from 1.
P(>0) = 1 - P(0) = 1 - (1 - p)^20 = . . .

The probability that the first student is <0.2s and the next 19 are all >0.2s is (0.100)(0.900)^19 = 0.0135.
The probability for exactly 1 out of 20 is that number multiplied by 20, because you don't care which of the 20 it is:
P(1) = n*p^1*(1 - p)^{n-1} = . . .
 
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