normal distribution notes

Question 1

normal distribution

Answer 1

bell shaped curve distribution

happens when :
the observations are independent
the sample is large enough

Question 2

characteristics of normal distribution curve

Answer 2

symmetric
univocal
bell-shaped
centered at the mean
total area under the curve is 1

Question 3

how can normal distribution curves be adjusted?

Answer 3

using two parameters —> mean and standard deviation

mean : changing mean shifts the curve left or right

standard deviation: changing so stretches or constricts the curve around the mean

Question 4

normal distribution notation

Answer 4

N(u,o) distribution
N = normal u= mean o = standard deviation

Question 5

central limit theorem

Answer 5

when the sample size is large enough, the distribution of the sample proportion (phat) will be approximately normal with mean p (population proportion) and standard deviation )sqrt p(1-p)/n)
if we know p, then we know how the sample proportion derives

Question 6

what is the relationship between the mean of the population proportion and the center of the distribution of p hat

Answer 6

mean p = center of the distribution of sample proportion

Question 7

standard scores

Answer 7

z-score
observed value- expected value/ standard deviation

x-u/o

quantifies the number of sd an observation falls from its mean or expected value

Question 8

random variables

Answer 8

assigns a # to each possible outcome

each random variable has a distribution that specifies how the possible values of the random variable are distributed

ex: X has a normal distribution with mean 6.5 ft and standard deviation 0.5 ft

Question 9

standard normal N

Answer 9

mean (u)= 0
sd(o) = 1

any time we standardize a normally distributed random variable x as z= x-u/o

Question 10

68,95,99.7 rule

Answer 10

68% of data falls between mean + 1 sd
95% fallers between mean + 2 sd
99.7 falls between mean + 3sd