Statistics exam 1 review

Variance is measured in no unit of measurement.

false - sigma squared /s^2 + units squared

£

the sum of

A mean can be either a parameter or a statistic.

true

A probability of one is certain to occur.

true

A probability of zero is impossible.

true

In probability, anything in between 0 and 1 is possible.

true

Standard deviation is measured in units (for example: centimeter).

true

The correct example of parameter is μ and σ .

true

Z- score is measured in no unit of measurement.

true

The mean and the standard deviation are given for non-standard distributions.

true- x- n (mu, o)- Mu^2, sigma (o) are given

S^2

sample variance symbol

Data is skewed if the mean and median are equal.

false

For probability, anything less than 5% is likely to happen.

false

To find the median, you add all the numbers together and divide by the number of entries in the data set.

false

Z- scores have a mean of 1 and a standard deviation of 0.

false - mean of 0, standard deviation of 1

S

sample standard deviation

List and define the four properties of a binomial distribution.

1) Independent trials 2) fixed number of trials 3) probability of success remains constant 4) two mutually exclusive outcomes

Find the value of z such that P(Z > z) = .025

1) given x -> z- score 2) look up in table 3) get probability 1 - 0.0250 = 0.9750 =1.96

There is an equal chance that (A) apples, bananas (B) cherries (C) dragon fruit (D) , elderberry (E) can be picked and they are mutually exclusive.

Find P(C) 1/5 Find p(C') 1- 1/5 = 4/5 Find P ( A or E) P(A) + P(E) = 1/5 + 1/5 = 2/5

Label and draw the sleekness for each type of graph

[ [ [ [ [ [ ——[————[—————[———— Mean. Median. Mode Left skewed

An airline company wants to survey its customers one day, so they randomly select 5 flights that day and survey every passenger on those flights.

Cluster sample

The acceleration of a car as it goes from 0-60 mph

Continuous

The volume of a sphere

Continuous

The number of Snapchat'a received in a day

Discrete

The number of limbs on a 2 year old tree is 21

Discrete

Probability ; a long term relative frequency whose value is between 0 and 1 In a class of 40 students , 8 are in the drama club and 12 are in the art club. If a student is selected at random , what is the probability that the selected student is :

Drama club= 8/40 divided by 8 = 1/5 Art club= 12/40 divided by 4 = 3/10

Calculate the expected value of the discrete data given in the frequency table below.

Expected value = m= £ x f(x) X 0 1 2 3 F(x) 0.17 0.14 0.36 0.33 0 (0.17) + 1 (0.14)+ 2 (0.36) + 3 ( 0.33) 0 + 0.14 + 0.72 + 0.99= (1.85) answer

Talia wants to play a basketball game at the carnival. The game costs the player $5 to play, and the player gets to take two long distance shots. If they miss both shots , they get nothing. If they make one shot, they get their $5 back. If they make both shots , they get $10 back. Here is the probability that the distribution of x = the amount of money Talia gains from playing the game. X= money gained - 5 0 5 P(x) 0.36 0.48 0.16 Given the 'mu' = -1 , calculate the standard deviation

M= -1 S^2 (0.36) + o^2 (0.48) + s^2 (0.16) 9+0+4 =13 13 - -1^2 = 13 -1 = 12 ——- \| 12 = 3.464

Which is not robust: resistant ?

Mean Mode

Which is robust/resistant ?

Median

Find the following given the sample data set 6,4,7,5,3 Mean Median Mode

Median -5 Mode - none Mean- 5 Range-4 Sample variance - s^2= 2.5 Sample standard Deviation- 2.5

Find the area to the right of 1.53 ( Must know how to solve without a calculator)

P( Z > 1.53) = 0.9370 1- 0.9370 = 0.0630

Find P( -1.24 < Z < 1.54)

P( z < -1.24) - P(z< 1.54) 0.9382 - 0.1075 =. 0.8307

Find the area to the left of 1.34

P(z<1.34) = 0.9099

Administrators at Riverview highs school surveyed 100 of their seniors to see how many seniors at the school felt about the lunches offered at the school. Population =? Sample=?

Parameter-Seniors Statistic-100 of the seniors

The State Department of transportation wants to know about the out of state vehicles that pass over a toll bridge with several lanes. A camera installed over one of the bridge photograph the license plate of every tenth vehicle that passes through the lane Population =? Statistic=?

Parameter= All vehicles using toll bridge Statistic= every 10th car that passes the lane with the camera

Lucia wants to know whether the food he serves in his restaurant is within a safe range of temperatures. He randomly selects 70 entrees and measures their temperatures just before he serves them to his customers Population=? Sample=?

Parameter= all the entrees Statistic= 70 entrees

'Mu'

Population mean

N

Population size

σ

Population standard Deviation

σ^

Population variance

Number on hockey jersey

Qualitative

Shapes of candy in a variety pack

Qualitative

How many phone calls have you made in the last 24 hours ?

Quantitative

Number of calories in a Donut

Quantitative

Iran ran out of time while taking a multiple choice test and plans to guess on the last 6 questions. Each question has 4 possible choices, one of which is correct. Let x = the number of answers ira correctly quested in the last 6 questions. What is the probability that he answers exactly 2 questions correctly in the last 6 questions.

Sample space ( 0, 1 , 2 , 3 ,4 , 5 , 6 ) q = 0.75 P= 0.25 n= 6 X = 2 PMF= ( n ) p^x q^n-x x P(X = 2) ( 6 ) 0.25^2 0.75^4 = 2 (15) (0.0625) (0.31640625) = 0.2966

A sample of the first 100 people admitted to the San Diego comic con resulted in 32% who said Superman is their favorite superhero ( parameter or statistic)

Statistic

In a national survey of high school students (grades 9-12) 47% of respondents reported that they had already chosen the college they plan to attend. (Parameter or statistic)

Statistic

A principle orders t shirts and wants to check to make sure they were printed properly. She checks 5 shirts from all ten boxes of t shirts that were ordered.

Stratified sample (some from all)

A teacher is interested in gathering information. While students are lined up for school pictures, that teacher passes out a survey to every 20th student.

Systematic sample (kth term)

23) Identify whether true or false ( make sure to memorize and be familiar with the concepts ) of false , address what makes it false. A) a mean is know as a statistic if it is computed from from the sample.

True

Z

Z -score

Find the 99th percentile of this distribution. X?

Z = 2.33

Assume the random variable X is normally distributed with a mean of 12 and a standard deviation of 5. Answer the following P(x->2

Z= x-m/σ = 2-12/5 = -10/5= -2.00 P(z<-2.00) =0.0228 -> 1- 0.0228= 0.9772

P(X<8)

Z= x-m/σ = 8-12/5 = -4/5 =-.80 ( go to the table) ( 0.2119 )

P(16<X<20)

Z=x-m/σ = 16-12/5 = 4/5 =0.80 = P(Z<0.80) = 0.7881 Z= x-m/σ = 20-12/5= 8/5= 1.60 = P(z<1.60= 0.9452 ( 0.1571 )

The department chair was interested in the average test one score for statistic classes. The average score of all the classes was 79% (Parameter or statistic)

parameter

q

probability of failure

P

probability of success

P( )

probability of success

Phone number

qualitative

x bar

sample mean (statistic)

n

sample size