stats final

probabiity luis will pass his stat test is .58. find the probability he will fail his stat test...

1-.58 =( .42)

dealt two cards without replacement from a shuffled pack of 52 playing cards. find the prob first card king and second card queen

1. "and" = multiplication formula 2. dependent or not? (YES, without replacement) 3. 4/52 x 4/51 *** without replacement

find the probabiity the fight selected arrived on time given that it was upstate airline flight

1. GIVEN = conditional formula 2. P(A given B) = probability (a and b)/p (B)

if one of 1010 people randomly selected, find the probability that the person is a man or a heavy smoker

1. OR = addition formula 2. p (A) + p(B) - (a and b at same time)

which score has higher relative position

1. calculate both z scores to standardized and compare

56% graduates get a job. among 6 randomly selected graduates, at least one finds a job

1. dependent or not? (not!) 2. write out prob choices 0,1,2,3,4,5,6 3. easier to do 1- p(x=0) 4. probability of success is .56 but prob of fail is .44 5. 1- (.44) ^6 (6 times this is the failure rate)

diet program varies between 6 lbs and 12 lbs, and is spread evenly over a range of possibilities, so there is a UNIFORM DISTRIBUTION. find the probability of the given range of lbs lost -more than 10

1. draw graph with square box and label 2. if the length is 6-12 then = 6 3. height must make box =1, so height = 1/6 4. more than 10 = between 10-12 5. so multiply new length: 2 x height 1/6 =1/3

a random sample of 250 students a university finds that these students can take a mean of 15.2 credit hours per quarter with a standard deviation of 2.3 credit hours. estimate the mean credit hours taken by a student each quarter using a 95% confidence interval

1. find corresponding z score to .95 --> common critical value of 1.96 2. plug into SAMPLE z score formula because its a random sample of 250 but make z=1.96 and solve for xbar

4 requirements of binomial distribution

1. fixed number of trials 2. trials independent 3. two categories (success/failrue) 4. probabilities must remain constant

the amount of snowfall in a certain mountain range is normally distributed with a mean of 89 inches and a sd dev of 14 inches. what is the probability that the mean annual snowfall during 49 randomly picked years will exceed 91.8inches

1. mu: 89 sd: 14 n: 49 x: 91.8 2. z formula but use SAMPLE formula, where denominator is sigma/Square root of n because "49 randomly picked years" 3. P (x>91.8) = 1.4 4. take z score and find area inside 1.0 and .4 to get .9192 5. because P(x>91.8) is area right of curve, need to do -> 1- p(x<91.8), so 1-.9192

a die with 8 sides is rolled. what is the prob of rolling a number less than 7

1. p(x<7) 2. p success/total (1,2,3,4,5,6) 3. 6/8 4. 3/4

the weight (in lbs) of 30 newborn babies listed below. find Q1

1. q1=.25 2. .25x30 (=7.5) 3. ROUND UP ROUND UP ALWAYS--> 8th position 4. count the 8th number in data set

random sample of 4000 US citizens yielded 2250 who are in favor of gun control legislation. how many citizens would need to be sampled for a 90% confidence interval to estimate the true proportion within 1%

1. sample size formula with p cap and q cap 2. find 90% confidence interval for n 1.645 3. z alpha over 2 = those in favor over total (p cap) 4. "within 1%" = SE .01 as decimal

find the probability of AT LEAST 2 girls in 8 births. independent and equal chances...

1. use binomial distribution 2. p(x> or equal to 1) --> 1-p(x< or equal to 2) 3. calculator to find binomial CDF "c or fewer" 4. 2nd --> varse --> binomcdf -trials: 8 -p: .5 (1/2) -x: 2

weekly salaries of teachers in one state normally distributed with mean of $490 and sd of $45. what is the probability that a randomly selected teacher earns more than $525 a week?

1. use z formula with normal sd 2. "more than 525" : x>525 --> change to 1- (x<525) 3. 1- z formula answer

what does it mean to score 85% on exam vs score in the 85 percentile in mathematics SAT

85% on exam= knew 85% of the content on exam 85 percentile = score was better than 85% of the scores of examinees on SAT

how to compute (9 4) 9 over 4 without division sign

=combination calculater: math --> prob --> 3 --> nCr (9 choose 4)

z0.02 find indicated value

asking for AREA, so look INSIDE chart for closest value and locate -2.05 and -2.06 and avg them

categorical v quanitivative and ex

categorical/qualititative data can be separated into categories with names/labels EX: male/female athletes quantitvative data is numerical data EX: weights of supermodels

continuous v discrete with EX

continuous: infinitely many possible values that can be associated with points on on a scale without gaps EX: temperature, weight, heigh, time discrete data is a finite number of possible values or a COUNTABLE number of possible values EX: score on a test of 100

what is the mean of a given probability distribution

expected value (like weighted mean but buttom is one) sum of multiplying x times p(x)

type 2 error

failed to reject but it was false

histogram v pareto

histogram: quantitative information about shapes of distributions (temperatrure, weight, amount of tv) Pareto chart: convey comparative information about relative standing of categorical data (favorite summertime activity)

what is usual/unusual z score

less than -2 or more than 2.0

how to find median

order from largest to smallest and cross out either side to get middle number

differentiate between population, parameter, sample, and statistci

population is a complete collection of all data and goes with parameter which is the numerical measurement describing characteristics of a pop (written as Mu and sigma) sample is a subset of members selected from a population and goes with statistic which is a numerical measurement describing sample characteristics (written X bar and S)

what does the standard deviation provide

provide understanding of individual points vary from the mean the variability/spread of data (since units not squared)

range or standard deviation?

range: sensitive to extreme values or outliers st dev: easier to understand spread, less affected by outliers

what is a random variable?

real #, not a sequence

type 1 terror

rejected h not but it was true

would a company want a process that provides a large or small variance?

small variance, since the this measure denotes consistency (close to average mean)

small sd v large sd

small: individual scores close to mean large: larger sd

when values converted to z score the mean and sd will always be...

the mean of z scores will be 0 and the sd of z scores will be 1

how to find z score

x score formula on formula sheet x is ex number, and m is the mean

what is a valid probability distribution

x's need to be between 0-1 p(x) need to add to 1 and be positive

x to represent possible sequence of heads and tails that can be obtained with 3 flipps. listed Xs (HHH, HHT....) and Probability of X (1/8)(1/8).... what is the probability distribution of the associated random variable (H)

x: number of successes or H's 3 p(x) how many times likely to occur 3/8

in a game you have 1/36 probability of winning $81 and a 35/36 prob of loosing $3. what is expected value??

xs: 81 and -3 p(x): 1/36 and 35/36 E = sum of (81x(1/36) and (-3(35/36)