SOLUTION: Let the random variable X follow a normal distribution with 𝜇= 80 and 𝜎2= 100. a.Find the probability that X is greater than 60. Draw a probability distribution graph.b. Find

Question 1178586: Let the random variable X follow a normal distribution with 𝜇= 80 and 𝜎2= 100. a.Find the probability that X is greater than 60. Draw a probability distribution graph.b. Find the probability that X is greater than 72 and less than 82.c. Find the probability that X is less than 55.d. The probability is 0.1 that X is greater than what number? e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this online calculator makes the solution to these problem easy.
https://davidmlane.com/hyperstat/z_table.html
it is based on z-scores.

the answer to your problems are shown below:

in these problems, the mean is 80 and the standard deviation is equal to the square root of the variance = sqrt(100) = 10.

a. Find the probability that X is greater than 60. Draw a probability distribution graph.

b. Find the probability that X is greater than 72 and less than 82.

c. Find the probability that X is less than 55.

d. The probability is 0.1 that X is greater than what number?

e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?

the calculator is very simple to use.
the main thing you have to do is to calculate the standard deviation or the standard error correctly.

in this problem, the standard deviation of the population is used.
since the standard deviation is the square root of the variance, then the standard deviation in this problem is square root of 100 = 10.

if you're dealing with a sample of the population of a certain size, then the standard error is used.

the formula for that is standard error = standard deviation / square root of sample size.

if you have to work with z-scores, the same calculator can be used.
in that case, the mean is 0 and the standard deviation is 1.

if you have any questions about that you still need to answer, let me know.

theo
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