normam distribution

Question 1

characteristics of normal distributions

Answer 1

• variable has to be continuous
• for a continuous variable, the area under the probability graph has to be 1
  (so to find P(170<X<190>), use integration to find the area between these values)
• y axis is the probability density

Question 2

the middle of the normal distribution curve is

Answer 2

the mean

Question 3

the larger the variance,

Answer 3

the wider the curve

Question 4

normal distribution format

Answer 4

X ~ N (mew, variance) (o^2)

Question 6

the curve has

Answer 6

points of inflection one standard deviation away from the mean
(where the curve changes from concave to convex)

Question 7

the normal distribution is

Answer 7

symmetrical, mean = mode = median

Question 8

68-95-99.7 rule

Answer 8

• 68% of data is within one standard deviation of the mean
• 95% of data is within two standard deviations of the mean
• 99.7% of data is within three standard deviations of the mean
• for practical purposes, we consider all data to lie within mew + or - 5(variance)

Question 9

what is the z value

Answer 9

the number of standard deviations above the mean

Question 10

how to find z value

Answer 10

(X - mean) / standard deviation

Question 11

what is the standard normal distribution

Answer 11

X ~N (0,1^2)
mean = 0
sd = 1

Question 12

P(a<Z<b) is the same as

Answer 12

P(z<b) - p(z<a)

Question 13

when can we use normal distribution from binomial distribution

Answer 13

• when the number of trials is large
  and the probability is close to 0.5

Question 14

how to set the mean and standard deviation from binomial distribution

Answer 14

mew = np

s.d = sqrt(np(1-p))