Question

Consider an arbitrary, continuous normal distribution with a given mean and standard deviation. Derive an integral...

Consider an arbitrary, continuous normal distribution with a given mean and standard deviation. Derive an integral function that gives the percentile of a particular value, X. The integration is analytical, yet it is often given a functional representation erf(). Look it up and plot the erf function in terms of the mean and standard deviation. Estimate the 25th and 75th percentile. Within how many standard deviations from the mean is 50% of the distribution?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given X with a normal distribution with mean 39.5 and standard deviation 5.0. a. What is...
Given X with a normal distribution with mean 39.5 and standard deviation 5.0. a. What is the probability that X is between 38.0 and 42.5? b. What value of X falls at the 85th percentile?
Tom's psychology test score is +1 standard deviation from the mean in a normal distribution. The...
Tom's psychology test score is +1 standard deviation from the mean in a normal distribution. The test has a mean of 60 and a standard deviation of 6. Tom's percentile rank would be approximately ______________. a. 70% b. cannot determine from the information given c. 84% d. 66%
Given a random variable X following normal distribution with mean of -3 and standard deviation of...
Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal. (1)Find the distribution of Y, i.e. μy,σy (2)Find the probabilities P(−4<X<0),P(−1<Y<0) (3)Find the probabilities(let n size =8) P(−4<X¯<0),P(3<Y¯<4) (4)Find the 53th percentile of the distribution of X
Considering a graphed pdf for a continuous normal distribution with mean μ and standard deviation σ,...
Considering a graphed pdf for a continuous normal distribution with mean μ and standard deviation σ, which of the following are true? Select one or more: a. If the mean is zero then the pdf of the normal distribution and standardised normal distribution will be the same b. A distribution with a lower σ will have an increased P(X=μ) c. A combination of adding constants to and multiplying each term in the sample space will affect the skewness of the...
Given a normal distribution with Mean of 100 and Standard deviation of 10, what is the...
Given a normal distribution with Mean of 100 and Standard deviation of 10, what is the probability that between what two X values (symmetrically distributed around the mean) are 80% of the values?
The Standard Normal Distribution with a mean of 0 and a standard deviation of 1 has...
The Standard Normal Distribution with a mean of 0 and a standard deviation of 1 has been used to calculate areas under the normal distribution curve. Originally, quality control analysts were content to confine all data within +/- three standard deviations from the mean. The Ford Motor Company in the mid 1980s decided to try to confine all data within +/- four standard deviations from the mean. Six Sigma, the newest quality venture, is trying to confine all data within...
A continuous random variable Z follows standard normal distribution. a) What is the mean of Z?...
A continuous random variable Z follows standard normal distribution. a) What is the mean of Z? b) What is the standard deviation of Z? c) Z=(x-10)/5 What is the distribution of X ?
Which of the following is false? The normal distribution is defined by two parameters, the mean...
Which of the following is false? The normal distribution is defined by two parameters, the mean and the standard deviation. In a normal distribution, the probability that the random variable X takes a particular value is zero. For a continuous random variable the probability associated with any values of the random variable is found by calculating the area under the relevant normal curve. For a normal distribution, approximately two thirds of the observations will fall within two standard deviations either...
Q1-. A normal distribution has a mean of 15 and a standard deviation of 2. Find...
Q1-. A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th percentile. Round your answer to two decimal places. Q2-.Tyrell's SAT math score was in the 64th percentile. If all SAT math scores are normally distributed with a mean of 500 and a standard deviation of 100, what is Tyrell's math score? Round your answer to the nearest whole number. Q3-.Find the z-score that cuts off an area...
Given a normal distribution with a mean of 125 and a standard deviation of 14, what...
Given a normal distribution with a mean of 125 and a standard deviation of 14, what percentage of values is within the interval 111 to 139? (4 points) 32% 50% 68% 95% 99.7%
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT