# Mat 120 probability

a statistic describes data taken from a _______
sample
a parameter describes data taken from a ______
population
after inspecting 18 lipsticks, 14 were red. Statistic or parameter?
statistic
data that cannot be arranged in an ordered scheme (consists of labels, categories) is of the ______ level of measurement
nominal
data that can be arranged in order, but differences are not significant (say, figuring the average) is of the ______ level of measurement
ordinal
data that can be arranged in order, differences are significant, but there is NO natural zero starting point is of the ______ level of measurement
interval
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data that can be arranged in order, differences are significant, and there is a natural zero starting point is of the ______ level of measurement
ratio
what kind of study simply looks at characteristics, but does not modify anything?
observational
what kind of study modifies something?
experiment
what kind of sampling? each member of the population has the same chance of selection
random
what kind of sampling? every possible sampling of the sample size n has a possibility of being chosen
simple random
what kind of sampling? every fifth
systematic
what kind of sampling? grabbing someone off the street you happen to see right then
convenience
what kind of sampling? subdividing a population into at least two groups that bear the same characteristics, then making sure to get a sample from each group
stratified
what kind of sampling? divide population into sections, then randomly select different sections for study
cluster
find the class midpoint of interval 40-59
49.5
questions 19-24 on practice test one!
done
find the mean: 10, 5, 12, 14, 2
8.6
you find the _______ by adding max and min and dividing that by 2
midrange
find the midrange: 12 15 9 2 5 77
39.5
the _____ is the number in the exact middle of the sorted list. (like, 12, 15, 18, 21, 24 — 18 would be this number)
median
to find the ______, subtract the min value from the max value
range
question 30
(edit stat list, 1-var stat, sx = sample standard deviation and sigma-population x (the one under sx) is the population standard deviation)

(variance is the sample deviation, squared)

find the area of a normal distribution graph that has a mean of 100, a shaded area starting at 102 and going to 126 and a standard deviation of 15
.4054 (use normalCDF)
engineers want to design seats that fit the hip breadths of 90% of men. they are normally distributed with a mean of 14.8in and a standard deviation of 1.1in. how wide can the widest hip breadth be and still fall into the 90% that fit?
16.2 (in, use InvNorm)
write this in p(hat) plus or minus E form.
0.489, 0.561
0.525 (plus or minus) 0.036
P-hat (I can’t do the hat on here) can be found by adding the two confidence intervals together and dividing them by two. E can be found by subtracting the smaller from the larger and dividing by two.
P(hat) can also equal what divided by what?
x, n (number divided by population/sample)
alpha (little fish looking thing) refers to what?
the area to the left of the normal distribution curve
A 90% level of confidence has α = 0.10 and critical value of zα/2 = 1.64.
A 95% level of confidence has α = 0.05 and critical value of zα/2 = 1.96.
A 99% level of confidence has α = 0.01 and critical value of zα/2 = 2.58.
A 99.5% level of confidence has α = 0.005 and critical value of zα/2 = 2.81
okay
find the margin of error: n= 550 x= 165 90% confidence.
.032 (the margin of error is the upper level limit minus the lower level, divided by half)
rejecting the claim that I have 6 fingers when I actually DO have 6 fingers is what type of error?
type I
failing to reject that I have 6 fingers when there is not evidence to support it is what type of error?
type II
reject?
type I
fail to reject?
type II
when looking at r in a linear regression (linreg ax+b) what does it signify?
correlation coefficient (You can tell which way the line/correlation is going by this number – negative means the line is going down, etc)
your sample size is less than 30 (n < 30 ) OR the population's standard deviation/variance is unknown. which do you use, z or t?
t (little samples)
_______ __ ________ = one less than n
degrees of freedom (t and z distributions)
the z score is x – mean divided by the standard deviation. the x is your data point. remember that sigma (the weird little sideways d) is the symbol for standard deviation.

also, remember standard deviations are like rulers. they are just a measuring device of how far away you’ve gotten from the mean, and in what direction

okay.
combinations that can be arranged in order (order matters) refers to a _________. order does not matter, it must be a __________
permutation, combination
a sample of four calculators is randomly selected from a group that contains 30 calculators with no defects and 16 with defects. what is the probability that at least one of these is defective? (3 decimals)
.832
the ____ _____ regression line minimizes the sum of the residuals squared
least squares
a faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model, Using the method of least squares, the faculty group obtained the following prediction equation,
Interpret the estimated y-intercept of the line.

y(hat)= 14000 + 2000x

>for an administrator who is rated zero, what is the raise?

14000
State whether the variable is discrete or continuous.
The number of cups of coffee sold in a cafeteria during lunch
discrete
discrete or continuous? The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
continuous
joan has a success rate of 75% and averages 10 calls a day. Margo has a success rate of 45% and averages 16 calls per day. what is the probability of success of exactly 6 calls for each? (joan first, then margo, 3 decimals)
something that is assumed, status quo, or a given would be a _____ hypothesis (ask yourself, “what do we currently accept?”)
null
something that is a claim, assertion or unknown is an _____ hypothesis
alternative (when the null is rejected)
Find the critical value zα/2 that corresponds to a 91% confidence level
1.7 (use invNorm. first take the complement (9%) and divide it in half, then that is your area for the invnorm)
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.

95% confidence; n = 2428, x = 1704

.0182 (use 1propZinterval, subtract upper limit from lower limit and divide by two)
Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 304 people, 20 people had hearing aids. (3 decimals)
.066 (20 divided by 304)
A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval. (3 decimals)
.438, .505
Determine whether the given conditions justify using the margin of error E = zα/2 σ/ when finding a confidence interval estimate of the population mean μ.

The sample size is n = 200 and σ = 19

yes (it’s over 30)
Determine whether the given conditions justify using the margin of error E = zα/2 σ/ when finding a confidence interval estimate of the population mean μ.

The sample size is n = 4, σ = 12.7, and the original population is normally distributed.

yes (it’s normally distributed)
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.

A random sample of 105 light bulbs had a mean life of 441 hours with a standard deviation of 40 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type. (round to whole numbers)

435, 447 (use Z interval)
How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.7 lb of the population mean, and the population standard deviation is known to be 28 lb. (whole number – 3 digit)
155 (invT)
98%; n = 7; σ = 27; population appears to be normally distributed. Find Z(alpha)/2 or t(alpha)/2 and round to 2 decimals
2.33, z
99%; n = 17; σ is unknown; population appears to be normally distributed. Find Z(alpha)/2 or t(alpha)/2 and round to 2 decimals
2.92, t
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 225 milligrams with s = 15.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
(round to whole #s)

215, 235 (use t interval because the sample is less than 30)
A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.
(round to one decimal)
67.7, 84.7 (use t interval, population less than 30)
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

α = 0.09 for a right-tailed test.

1.34 (use inv norm and plug in .91, because that is the area to the left)
Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is not sufficient evidence to support the claim that the mean is less than 30 miles per gallon.

B) There is not sufficient evidence to support the claim that the mean is greater than 30 miles per gallon.

C) There is sufficient evidence to support the claim that the mean is less than 30 miles per gallon.
Correct Response
D) There is sufficient evidence to support the claim that the mean is greater than 30 miles per gallon

d
A medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I error for the test.

A) Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually different from 6%.

B) Reject the claim that the percentage of children who suffer from the disorder is different from 6% when that percentage really is different from 6%.
Correct Response
C) Reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.

D) Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.

c
You wish to test the claim that μ ≠ 47 at a level of significance of α = 0.01 and are given sample statistics and Compute the value of the test statistic. Round your answer to two decimal places.
2.65 (z test, look at the Z)
Suppose you are using α = 0.01 to test the claim that μ ≤ 47 using a P-value. You are given the sample statistics and Find the P-value.
3 decimals.
.004 (z test, think about which side this distribution faces… which tail?
The brand name of a certain chain of coffee shops has a 54% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that exactly 4 of the 10 Coffleton residents recognize the brand name.
.169 (use binomPdf “exactly”)
A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
.377 (use binomCdf “at least”)
The probability that z lies between 0.7 and 1.98 (4 decimals)
.2181 (normalcdf)
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 (denoted by negative numbers) and some give readings above 0 (denoted by positive numbers). Assume that the mean reading is 0 and the standard deviation of the readings is 1. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.

If 7% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. (2 decimals)

1.48 (use invnorm and remember, the readings were too HIGH, so most of the things fall to the LEFT of that line in the distribution curve)
you have a 1/36 probability of winning \$94 and you have a 35/36 probability of losing \$8. what is your expected value?
In a study, 43% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health
.119 (use binomcdf, cdf is cumulative to everything to the LEFT of the “upper value”. when plugging in your x value, you want to choose the “most”. in the case of “at least”, you would choose the complement, in the case of “less than”, you would choose the plain number. binomPDF is obviously for EXACT numbers)
A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220.
.381
Find the critical value zα/2 that corresponds to a 91% confidence level
1.70 (use invnorm, remember that in each tail, there is half of the “residual” or “leftovers” because this is a two-tailed test. SO, you must take half the complement as the area)
Only 5 percent of all 2010 individual tax returns claimed a deduction for medical expenses. Find the probability that at least 1 of the 3 returns will claim a deduction for medical expenses.
.143 (use binompdf to find the complement – that is, the probability that you will find 0 that claim a deduction, and then subtract that number from one)
A dish contains 12 pieces of candy. Eight of the pieces are covered with dark chocolate and the other 4 with light chocolate. If 4 pieces are randomly selected from the dish, what is the probability that all will be covered with dark chocolate?
.141 (use 8x7x6x5 divided by 12x11x10x9)
If A is the event that you will get an A on this test, and B is the event that you will obtain a B on the test, then the events A and B are
A)
mutually exclusive and independent.

B)
not mutually exclusive.

C)
independent.

D)
mutually exclusive and dependent.

d
The manager of a movie theater has found that 38 percent of its customers purchase a drink, and 28 percent purchase both a drink and a bag of popcorn. Determine the probability that a customer who purchased a drink at this theater also purchased popcorn. (2 decimal)
.74 (divide .28 by .38, or rather, divide the x by the given)
A basket contains 20 eggs, 13 of which have white shells and 7 have brown shells. Determine the number of ways that 3 white and 5 brown eggs can be selected from the basket.
6006 (13 ncr 3 times 7 ncr 5)
One card is selected randomly from a standard deck of 52 cards. The probability of selecting a red card or an ace is
.54 (28 divided by 52)
Twelve percent of infants treated by a certain pediatrician are given a test for a bacterial infection. When an infant is tested, the probability is 0.60 that the baby has the bacterial infection. The probability that an infant will be tested for the infection and will actually have it is………
.072 (AND = multiply)
A graduating senior is going to purchase a new suit, a shirt and a tie for upcoming job interviews. A clothing store has 10 suits, 5 shirts and 20 ties that are suitable for the student. How many different ways could he make his clothing selections at this store?
1000 (multiply all 3 together)
A train station has two beverage machines, A and B. A is used for 58 percent of the beverage purchases made at the station. Fifteen percent of the time machine A overfills a cup, while 10 percent of the cups dispensed by machine B are overfilled. Determine the probability that a cup of beverage purchased at the station will be overfilled.
.129 (remember to get the complement of 58% to figure out the 10% that B overfills! then just add the two together)
There are 7 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?
210 (7 npr 3)
How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?
2520 (7 npr 5)
There are 8 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?
56 (8 ncr 5)
A study conducted at a certain college shows that 54% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. (3 decimals)
.979 (find the COMPLEMENT, because you want to know at LEAST one. so find the complement of the probability of finding NONE. multiply that number… so .46 to the 5th power)
In one town, 75% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance?
.316 (.75 to the 4th power)
Classify the events as dependent or independent. Events A and B where
P(A) = 0.6, P(B) = 0.3, and P(A and B) = 0.17
dependant
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places.
.006 (4/52 times 4/51)
A combination lock is opened with the correct sequence of four numbers between 0 and 29 inclusive. If a number can be used more than once, what is the probability of guessing those four numbers and opening the lock with the first try?
1/810000 (30 to the fourth power)
According to police sources, a car with a certain protection system will be recovered 90% of the time. If 100 stolen cars having this protection system are randomly selected, what is the standard deviation of the number of cars recovered?
3 (sigma = square root of npq)
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain rout is approximately normal with a mean of 15.5 and a standard deviation of 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases?
.8944 (use normalcdf)
The body temperatures of adults are normally distributed with a mean of 98.6 degrees F and a standard deviation of 0.60 degree F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4 degrees F.
.9772 (use the z blah blah blah)