(5) normal distribution

Question 1

What are the percentages about normal distribution?

Answer 1

• 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.

Question 2

How do you use inverse normal distribution function?

Answer 2

It uses a probability but must be less than.

Question 3

What is the standard normal distribution?

When can it be used?

Answer 3

-This is used to standardise normally distributed variables .

z=X-m/ std

Used when there is limited information.

Question 4

What must you do when approximating a binomial distribution with normal distribution?

Answer 4

-You must apply half continuity correction.

Question 5

How do you move from the population to a sample distribution of the means?

What must be remembered by this?

Answer 5

-std deviation squared / number in sample.
population divide by sample size.

-must remember to square root the whole thing

Question 6

How do you use the standard normal distribution when using a sample.

Answer 6

z= x-m/ std/root n

Question 7

How do you carry out a hypothesis test using normal distribution?

Answer 7

• 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

Question 8

What is the relationship between the mean and the sample mean?

How is the variance impacted between the population and sample?

Answer 8

• The sample mean will average out to the population mean.

- With a higher sample size the possible range of variances is lower.

Question 9

How can you use the standard normal distribution to make a hypothesis test?

Answer 9

-Work out the corresponding number of the area on the standard normal distribution and then uncode it using z=X-m/std/ root n

Question 10

What is the normal distribution used for?

What is the mean?

Answer 10

-Used for continuous data.

Mean=mode=median.

Question 11

What is significant about the calculator when working out normal distribution?

Answer 11

-Calculator does for less than.

Question 12

where does the normal distribution have points of inflexion?

Answer 12

mean+ std

mean - std

Question 13

What is another way of saying P(Z<a></a>

Answer 13

0 with line through (a)

Question 14

What are the conditions of a normal approximation?

Why is this?

Answer 14

• if n is large
• p is close to 0.5

-because normal distribution is symmetrical.

Question 15

How do you calculate the approximate mean and std value?

Answer 15

• mean = np

- st square root of np(1-p)

Question 16

What is a strategy to apply the continuity§y correction?

Answer 16

-draw the box with the 0.5 either side and identify the area needed.

Question 17

What are the steps to perform hypothesis testing with normal distribution?

Answer 17

• 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.