(5) normal distribution Flashcards
(17 cards)
What are the percentages about normal distribution?
- Approx 68% of the data lies within 1std deviation of mean
- Approx 95% of data lies within 2std of mean
Approx 99.7% lies within 3std of mean.
How do you use inverse normal distribution function?
It uses a probability but must be less than.
What is the standard normal distribution?
When can it be used?
-This is used to standardise normally distributed variables .
z=X-m/ std
Used when there is limited information.
What must you do when approximating a binomial distribution with normal distribution?
-You must apply half continuity correction.
How do you move from the population to a sample distribution of the means?
What must be remembered by this?
-std deviation squared / number in sample.
population divide by sample size.
-must remember to square root the whole thing
How do you use the standard normal distribution when using a sample.
z= x-m/ std/root n
How do you carry out a hypothesis test using normal distribution?
- Step 1, set out h0: which is the original mean.
- Step 2, h1: is the claim of what has happened to the mean.
- Step 3, convert population distribution to sample distribution
- Step 4, then test the other mean statistic with the sample size
- Step 5 work out the probability and see if this fits in the critical region
- Step 5 sufficient or insufficient evidence to reject h0 or h1
- Step 6 then link it back to the end
What is the relationship between the mean and the sample mean?
How is the variance impacted between the population and sample?
- The sample mean will average out to the population mean.
- With a higher sample size the possible range of variances is lower.
How can you use the standard normal distribution to make a hypothesis test?
-Work out the corresponding number of the area on the standard normal distribution and then uncode it using z=X-m/std/ root n
What is the normal distribution used for?
What is the mean?
-Used for continuous data.
Mean=mode=median.
What is significant about the calculator when working out normal distribution?
-Calculator does for less than.
where does the normal distribution have points of inflexion?
mean+ std
mean - std
What is another way of saying P(Z<a></a>
0 with line through (a)
What are the conditions of a normal approximation?
Why is this?
- if n is large
- p is close to 0.5
-because normal distribution is symmetrical.
How do you calculate the approximate mean and std value?
- mean = np
- st square root of np(1-p)
What is a strategy to apply the continuity§y correction?
-draw the box with the 0.5 either side and identify the area needed.
What are the steps to perform hypothesis testing with normal distribution?
- step 1, work out the sample varaince
- Step 2, define variable
- step 3, create X bar model
- step 4, Outline hypothesis.
- Step 4 use number in question to work out probability
- Step 5 identify if this is in critical region.
- Step 6 write conclusion in context.
