STAT FINAL Module 2
To find the left area z-score of a curve using norm.inv
(1-probability, mean, standard_dev)
Binomial Expirements
- Trials - Two Outcomes - Independence
The proportions of families with various numbers of children age 18 or under in a small town are given in the following table. One family is randomly selected from this town. Find the probability that the selected family has at least 3 children age 18 or under.
0.1
P ( x > # )
1-NORM.DIST(x,mean,std,T)
P(x≤ value)
= BINOM.DIST(x,n,p,TRUE)
p(X>value)
= BINOM.DIST(x,n,p,TRUE)
An inspection of 160 parts made from two production lines at a factory yields the following table. A part is randomly selected from these 160 parts. The probability that this part is defective or is made from production line 2 is about
=(13+90-8)/160
The table shows the results of a survey in which 90 dog owners were asked how much they have spent in the last year for their dog's health care, and whether their dogs were purebred or mixed breeds. Find the probability that a randomly selected dog owner spent at least $100 on health care and the dog was a mixed breed.
=15/90
The table shows the results of a survey in which 90 dog owners were asked how much they have spent in the last year for their dog's health care, and whether their dogs were purebred or mixed breeds. Find the probability that less than $100 was spent on a randomly selected dog's health care in the last year.
=40/90
An inspection of 160 parts made from two production lines at a factory yields the following table. A part is randomly selected from these 160 parts. Given that a randomly selected part is from production line 1, find the probability that it is defective.
=5/70
A woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%. Which of the following shows the correct EXCEL formula to find the probability that in any one month, at least three of the tickers that the woman buys are winning tickets?
=BINOM.DIST(2, 20, 0.10, TRUE)
You are taking a multiple-choice quiz that consists of five questions. Each question had four possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. Which of the following shows the correct EXCEL formula to compute the probability of guessing less than three answers correctly.
=BINOM.DIST(2, 5, 0.25, TRUE)
A woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%. Which of the following shows the correct EXCEL formula to compute the probability that in any one month, exactly 5 of the tickets that the woman buys are winning tickets?
=BINOM.DIST(5, 20, 0.10, FALSE)
p(x=value)
=BINOM.DIST(x,n,p,FALSE)
In a lottery game, players pay $2 for a ticket. Out of each batch of 1000 tickets, 1 ticket wins $500, 10 win $100, and 89 of them win $10. The remaining tickets have no prize awarded. Let the random variable X be the profits earned from the lottery. Here is the probability distribution for X: Which of the following excel function calculates the expected value to the player that purchases one of these tickets?
=SUMPRODUCT(B2:E2, B3:E3)
t distribution
A distribution specified by degrees of freedom used to model test statistics for the sample mean, differences between sample means, etc. where IT (' s) is (are) unknown
probability distribution function
A table that gives the probabilities for each value that a random variable can take on
The score made by a particular student on a national standardized exam is the 65th percentile. This means that
About 65% of all scores on the exam were lower than his.
Probability of guessing exactly ten answers correctly
BINOM.DIST(__,__,__,TRUE)
Probability of guessing less than ten answers correctly
BINOM.DIST(__,__,__,TRUE)
Standard Deviation
Determines data grouping around the mean the higher the standard deviation the flatter and wider the set is
Event
Ex: Let event A be the event that a even number is rolled A={2,4,6}
Outcome
Ex: Rolling a 1 on die
Probability
Ex: The probability of rolling an even number is 50% 50%=0.50=1/2
standard normal distribution
M/mean=0 Sigma/standard deviation =1
P (#<x<#)
NORM.DIST(b,mean,std,t)- NORM.DIST(a,mean,std,t)
P ( x < # )
NORM.DIST(x,mean,std,T)
Probability symbol
P
Calculating Probability for equally likely outcomes
P(A)= (# of outcomes in A)/(total # of outcomes in the sample space) P (A)= 3/6= 1/2= 0.50= 50%
Standard deviation
Sigma STD.DEV(__,__,__)
Central Limit Theorem
The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.
If the z-score corresponding to the weight of a newborn baby is 3, which of the following statements best describes the newborn's weight?
This is a very heavy baby in comparison to other newborn babies.
NORM.INV(probability, mean, standard_dev)
When you know the area under the curve but want to find the z-score
normal distribution
a bell-shaped curve, describing the spread of a characteristic throughout a population
random variable
a variable whose value is a numerical outcome of a random phenomenon
NORM.DIST function
always is true!
z-scores when positive
bigger than the mean
Finding z-score that corresponds to the confidence level
confidence level= 1-alpha alpha= 1- conf level alpha/2 Norm.Inv (1-alpha/2,0,1)
Expirement
ex: rolling a die
z-score
how much a value differs from the standard deviation
Confidence Intervals are based on the normal distribution
if the population standard deviation is known or if the sample size is greater than or equal to 30
z-scores when negative
lower than the mean
degrees of freedom (df)
n-1
Contingency Tables
provide a format to display the frequencies of qualitative variables
Sigma Xbar = standard error
sigma/square root of sample size
Mean
sum of x*p(x)
Sample Space (Probability)
the set of all possible outcomes Ex: s={1,2,3,4,5,6,}
Which of the following random variables is continuous?
the weight of a baby giraffe