Stat study guide 101
5.1
Z is the standard normal random variable it has a mean= 0 and sd = 1
(-10,000 is lower bound, 10,000 is upper bound if not given otherwise)
Normal curve:
The mean, median and mode are equal total areas=1
Symmetric and bell shaped never touches the x axis
Z= Value-Mean/ standard deviation
Properties of the standard normal distribution: cumulative area is close to 0 for z scores close to z= -3.49 cumulative area increases as the z scores increase cumulative area for z=0 is 0.5000 cumulative area is close to 1 for z-scores close to z=3.49
standard curve to left: normalcdf(-10,000, z=) standard curve to right: normalcdf (z=, 10,000)
Standard curve in between: normalcdf( z left, z right)
5.2
Probability for normal distribution
= normalcdf( upper bound, lower bound, mean, sd)
Z= Value- Mean/SD
5.3
10.75% = .1075
=invNorm(z score)
Ex: invNorm(0.3632) = -0.35
Example 2: find the z score that has 10.75% of the dist. area to the right
1- 1.075 (because its everything to the right)= .8925 invNorm(.8925)= 1.24
Percentiles:
P5: invNorm(.005)= -1.645
P50:invNorm(.5)= 0
P90:invNorm(.9)= 1.28
Transforming a z-score to an x value x= mean + z score(sd)
Ex: z=1.96 mean=9 sd=2 x= 9 + 1.96(2)= 12.92
For a specific data value: invNorm(z score area, mean, sd) or transform x value
5.5
Sampling distribution: the probability distribution of a sample statistic that is formed when samples of size n are repeatedly taking from a population.
Binomial distribution: if np>5 or nq>5 use normal distribution to apporximate x
= sq rt of npq
Ex: n-45, p=0.62, q= 0.38 np= 45(0.62)= 27.9 and nq + 45(0.38)=17.1 sq rt of npq= sq rt of 45 x 0.62 x 0.38 =3.26 ( approximating distribution of x)
Continuity correction: (moving left or right .5 based on graph) ex: probability of getting between 270 and 310 successes inclusive = 269.5 < x 157.5 probability of getting fewer than 63 successes=
Z is the standard normal random variable it has a mean= 0 and sd = 1
(-10,000 is lower bound, 10,000 is upper bound if not given otherwise)
Normal curve:
The mean, median and mode are equal total areas=1
Symmetric and bell shaped never touches the x axis
Z= Value-Mean/ standard deviation
Properties of the standard normal distribution: cumulative area is close to 0 for z scores close to z= -3.49 cumulative area increases as the z scores increase cumulative area for z=0 is 0.5000 cumulative area is close to 1 for z-scores close to z=3.49
standard curve to left: normalcdf(-10,000, z=) standard curve to right: normalcdf (z=, 10,000)
Standard curve in between: normalcdf( z left, z right)
5.2
Probability for normal distribution
= normalcdf( upper bound, lower bound, mean, sd)
Z= Value- Mean/SD
5.3
10.75% = .1075
=invNorm(z score)
Ex: invNorm(0.3632) = -0.35
Example 2: find the z score that has 10.75% of the dist. area to the right
1- 1.075 (because its everything to the right)= .8925 invNorm(.8925)= 1.24
Percentiles:
P5: invNorm(.005)= -1.645
P50:invNorm(.5)= 0
P90:invNorm(.9)= 1.28
Transforming a z-score to an x value x= mean + z score(sd)
Ex: z=1.96 mean=9 sd=2 x= 9 + 1.96(2)= 12.92
For a specific data value: invNorm(z score area, mean, sd) or transform x value
5.5
Sampling distribution: the probability distribution of a sample statistic that is formed when samples of size n are repeatedly taking from a population.
Binomial distribution: if np>5 or nq>5 use normal distribution to apporximate x
= sq rt of npq
Ex: n-45, p=0.62, q= 0.38 np= 45(0.62)= 27.9 and nq + 45(0.38)=17.1 sq rt of npq= sq rt of 45 x 0.62 x 0.38 =3.26 ( approximating distribution of x)
Continuity correction: (moving left or right .5 based on graph) ex: probability of getting between 270 and 310 successes inclusive = 269.5 < x 157.5 probability of getting fewer than 63 successes=