MAT 232 Exam II
For the purposes of constructing modified boxplots, outliers are defined as data values that are above Upper Q 3 by an amount greater than 1.5 times IQR or below Upper Q 1 by an amount greater than 1.5 times IQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.
.007
round to the nearest thousandth
0.8756777 round to 0.876
round to the nearest hundredth
0.8756777 round to 0.88
Round to the nearest tenth
0.8756777 round to 0.9
In a certain instant lottery game comma the chances of a win are stated as "5 in 19." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
1) "in"= 5/19= .263
Among 6234 cases of heart pacemaker malfunctions, 335 were found to be caused by firmware, which is software programmed into the device. a. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 6234 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? b. Is this procedure likely to result in the entire batch being accepted?
1) 6234-335= 5899 are not caused by firmwire 2) 5899/6234= .946 3) .946 x 5898/6233 (because they are selected without replacement) = .895 4) .895 x 5897/6232= .847 .847 is the total answer because you had to repeat the process three times without replacement.
In a study of helicopter usage and patient survival, among the 41,023 patients transported by helicopter, 222 of them left the treatment center against medical advice, and the other 40,801 did not leave against medical advice. If 60 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?
1) Find the probability of people of people that did not leave the treatment center against medical advice: 40.,801/41,023 =.9945884016 2) BECAUSE IT SAYS WITHOUT REPLACEMENT= .9945884016^60= .722 *If it was WITH replacement, it would have been subtracted 60 times. *Typically, bigger numbers= exponents ad smaller=subtraction.
Binomial Distribution rules
1) Fixed number of trials 2) Independent Trials 3) Must be classified into success or failure 4) The probability of success remains the same in all trials. (Discrete Random Variable)
Find the indicated critical value. z 0.04
1) Put value into probability part of normal calc on stat crunch 2) since, it's positive, it is to the right, therefore, use GREATER THAN symbol, (if it was left, use less than) =1.75
Among 8437 cases of heart pacemaker malfunctions, 472 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 8437 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
1) Subtract the total from the amount of malfunctions--- 8437-472 =7965 2) Divide 7965 by the total 7965/8437= .9440559441 3) Subract 1 from 7965 and 8431 and divide (do this two times) and multiply the products of all three. = .841 4) It is likely for this batch to be accepted.
There were 3,000,000 skydiving jumps and 21 of them resulted in death. Find the probability of NOT dying when making a skydiving jump.
1) Subtract total from deaths 3,000,000-21 = 2,999,979 2) Divide P(not dying when making a skydiving jump) = 2,999,979/ 3,000,000 = 0.999993. = complement of A
Probability Distributions rules
1) X is numeric 2) p(X) is greater than zero and less than 1 3) (Summation) P(x)=1
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 314 267 248 147 Order Not Accurate 31 57 36 13 If three different orders are selected, find the probability that they are all from restaurant Upper A.
1) add them all up = 1113 2) add up values from rest A= 345 3) Divide Rest A by all the values = 345/1113= .3099730458 4) Multiply that by itself TWICE= .0298
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 324 274 244 142 Order Not Accurate 38 60 37 13 If one order is selected, find the probability of getting an order from Restaurant A or an order that is accurate. Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events?
1) add up all numbers 2) add up rest a and all other orders accurate 3) Divide = .902
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 146 subjects with positive test results, there are 29 false positive results; among 158 negative results, there are 5 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana.
1) add up the total 146+158 2) add up the marijuana negatives 29+158 3) Divide that
The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. Use the range rule of thumb to identify a range of values that are not significant. The maximum value in this range is ______ girls.
1) find the mean 2) find the standard deviation (square and add, then square root the product subtracted by the mean squared) 3) max= mean-2(standard dev) 4) min= mean+2(standard dev)
For a certain casino slot machine comma the odds in favor of a win are given as 27 to 73. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
1) it says "to" relative probability-- add 27 and 73 =100 2) divide 27 by 100
In a state's Pick 3 lottery game, you pay $1.49 to select a sequence of three digits (from 0 to 9), such as 222. If you select the same sequence of three digits that are drawn, you win and collect $499.35. Complete parts (a) through (e).
1) selections = 1000 2) probability= 1/1000= .001 3) Net profit= amount possible- invested = 497.86 4) Expected value= (net profit x smallest dec) + (amount invested x bigger dec)
The concusions of the central limit theorem
1) the distribution of sample X will, as the sample size increases, approach a normal distribution 2) The mean of the sample distribution will be the same mean as the original distribution X. 3) The standard deviation of the sample distribution will be different. It will depend on the sample size n and be equal to ORIGINAL STANDARD DEVIATION/ SQUARE ROOT OF THE SAMPLE SIZE.
An elevator has a placard stating that the maximum capacity is 1288 lblong dash8 passengers. So, 8 adult male passengers can have a mean weight of up to 1288 divided by 8 equals 161 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 161 lb. (Assume that weights of males are normally distributed with a mean of 167 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe?
1) use the normal calc 2) standard dev= 32/ square root of 8 3) Use GREATER THAN symbol. = 0.7021 No, the elevator is not safe because there's a 70% chance that 8 people will overload it.
P(A or B) = P(in a single trial, event A occurs OR event b occurs, OR both)
Addition Rule
Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size nequals15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain. Choose the correct answer below. A. Yes; the sample size must be over 30 for the sample means to be normally distributed. B. No; the samples are collected randomly, so the sample means will be normally distributed for any sample size. C. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size. D. No; as long as more than 30 samples are collected, the sample means will be normally distributed.
C. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size.
_________ is any event combining two or more simple events and uses multiplication or addition rule.
Compound event
Events A and B are _______ if they cannot occur at the same time.
Disjoint
Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child. Complete parts a through d below.
Father =0 mother on son= 0.5
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 310 278 236 121 Order Not Accurate 36 60 31 13 If two orders are selected, find the probability that they are both from Restaurant D. a. Assume that the selections are made with replacement. Are the events independent? b. Assume that the selections are made without replacement. Are the events independent? a. Assume that the selections are made with replacement. Are the events independent? The probability of getting two orders from Restaurant D is b. Assume that the selections are made without replacement. Are the events independent? The probability of getting two orders from Restaurant D is
If it's independent and with replacement= multiply the probability by itself.= 0153, it is independent because the first order does not affect the other. If it's dependent and without replacement= get the first probability and subtract 1 from the total numbers of orders from rest D and the total numbers of orders in general. 134/1085 x133/1084= .0156, and it is not independent, it's dependent because the first order does affect the second one.
Which of the following is not a commonly used practice? a. If the original population is not normally distributed and n > 30, the distribution of the sample means can be approximated reasonably well by a normal distribution. B.The distribution of sample means gets closer to a normal distribution as the sample size n gets larger. C.If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed. D. If the distribution of the sample means is normally distributed, and n > 30, then the population distribution is normally distributed.
If the distribution of the sample means is normally distributed, and n > 30, then the population distribution is normally distributed.
A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution? The researcher collects more than 30 samples. If the population of statistics students has a normal distribution. If the population of grade-point averages has a normal distribution. The sample has more than 30 grade-point averages.
If the population of grade-point averages has a normal distribution. AND The sample has more than 30 grade-point averages.
The ________ states that as a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability.
Law of Large Numbers
P( A and B) P(event A occurs in a first trial and event B occurs in a second trial) P( B/A)
Multiplication Rule
Is a z-score an area under the normal curve?
NO
Are they disjoint? Event A- Randomly selecting someone taking a statistics course Event B- Randomly selecting someone who is female
No, because the selected person can be both.
Determine whether or not the procedure described below results in a binomial distribution. If it is not binomial, identify at least one requirement that is not satisfied. Seven hundred different voters in a region with two major political parties, A and B, are randomly selected from the population of 8000 registered voters. Each is asked if he or she is a member of political party A, recording Yes or No.
No, the trials are not independent and the sample is more than 5% of the population.
How to find prob of success
Number of favorable causes/ total number of possible cases
_____ means the probability of success.
P
Formal multiplication rule
P( A and B) = P(A) x P( B/ A) multiply the probability of event A by the probability of event B, but be sure that the probability of event B is found by assuming that event A has already occurred.
Formal Addition Rule Formula
P(A or B) = P(A) + P(B) - P(A and B) We must add in such a way that the outcome is counted only once.
Formula for Relative Frequency Approximation of Probability
P(A)= number of times A occurred _________________________________________________ number of times the procedure was repeated
P(A)
Probability of event A
P(--A--)
Probability of event A does not Occur (complement)
________ means the probability of failure.
Q
Find the probability of dying when making a skydiving jump In a recent year, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.
RELATIVE FREQUENCY APPROACH: P(skydiving death) = number of deaths _________________________ total number of skydiving jumps 21/ 3,000,000 = 0.000007 Here the classical approach cannot be used because two outcomes (dying, surviving) are not equally likely.
A main goal in statistics is to interpret and understand the meaning of statistical values. The _______ can be very helpful in understanding the meaning of the mean and standard deviation.
Range rule of thumb
If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. This represents the _______.
Rare event rule
Formula for Classical Probability
Requires equally likely outcomes A procedure has n different simple events that are equally likely, and if event A can occur in different ways, them P(A) = number of ways A occurs/ number of different simple events = s/n
Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 23 in. and a standard deviation of sigma equals 1.2 in. These data are often used in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater)less than or equals0.01 and a value is significantly low if P(x or less)less than or equals0.01. Find the back-to-knee lengths separating significant values from those that are not significant. Using these criteria, is a back-to-knee length of 25.1 in. significantly high?
SMALLER NUMBERS ON THE LEFT, LARGER ON THE RIGHT greater= 20.2 less than= 25.8
How to find prob of failture
Subtract 1 from success
For 100 births, P(exactly 57 girls)equals0.0301 and P(57 or more girls)equals0.097. Is 57 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.
The RELEVANT probability is P(57 or more girls), so 57 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05.
Which of the following is NOT a conclusion of the Central Limit Theorem? A. The distribution of the sample data will approach a normal distribution as the sample size increases. B.The mean of all sample means is the population mean mu. C.The distribution of the sample means x overbar will, as the sample size increases, approach a normal distribution. D.The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.
The distribution of the sample data will approach a normal distribution as the sample size increases.
Which of the following is NOT a requirement for a density curve?
The graph is centered around 0.
What does P(B|A) represent?
The probability of event B occurring after it is assumed that event A has already occurred.
The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical? Number of girls x=1,2,3 P(x)= 0.125, 0.375, 0.375, 0.125
The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are numerical.
For 100 births, P(exactly 56 girls)equals0.0390 and P(56 or more girls)equals0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.
The relevant probability is P(56 or more girls), so 56 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05.
When three children are born, the sample space of genders is (bbb, bbg, bgg, gbb, gbg, ggb, ggg). If boys and girls are equally likely, then those eight sample events are equally likely. Find the probability of getting three children all of the same gender when three children are born.
The sample space includes eight equally likely outcomes, and there are exactly two outcomes in which the three children are of the same gender: bbb and ggg. So, we use the CLASSICAL APPROACH. P(three children of the same gender) = 2/8= 1/4= 0.25
Central Limit Theorem
The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.
Are they disjoint? Event A- Randomly selecting someone for a clinical trial who is male Event B- Randomly selecting someone for a clinical trial who is female
Yes, because they cannot occur at the same time. The selected person cannot be both.
If you are asked to find the 85th percentile, you are being asked to find _____.
a data value associated with an area of 0.85 to its left
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.94 probability of working correctly when a voltage surge occurs. Complete parts (a) through (c) below. a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television?
a. (1-.94) x (1-.94) = 1- 0.0036 = 9964 b. .94 x.94 = .8836
When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 19 or to bet $15 that the outcome is any one of the three possibilities 00 comma 0 comma or 1. The gambler knows that the expected value of the $15 bet for a single number is negative 0.79 cents. For the $15 bet that the outcome is 00 comma 0 comma or 1, there is a probability of 3/38 of making a net profit of $45 and a 35/38 probability of losing $15. a. Find the expected value for the $15 bet that the outcome is 00 comma 0 comma or 1. b. Which bet is better: a $15 bet on the number 19 or a $15 bet that the outcome is any one of the numbers 00 comma 0 comma or 1? Why?
a. (45x 3/38)- (15x35/38) = -10.26 b. The single number bet is better because it is greater than the multiple number bet.
There is a 0.9987 probability that a randomly selected 29-year-old male lives through the year. A life insurance company charges $154 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100 comma 000 as a death benefit. Complete parts (a) through (d) below. a. From the perspective of the 29-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? b. The value corresponding to not surviving the year is c. If the 29-year-old male purchases the policy, what is his expected value? d. Can the insurance company expect to make a profit from many such policies? Why?
a. -154 (negative amount invested) b. .99846 (subtract 1 from p) c. -24, (.99846x.0013)-(154x.99846) d. Yes, 24, (just the opposite of the expected value--switch the sign).
For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are a. significantly high (or at least 2 standard deviations above the mean). b. significantly low (or at least 2 standard deviations below the mean). c. not significant (or less than 2 standard deviations away from the mean).
a. 0+2(1)= 2 (put it in in statcrunch as greater than and = 0.02275013x100= 2.28% b. 0-2(1)= -2 (put in statcrunch as less than and = 0.02275013x100= 2.28% c. 2.28+2.28-100= 95.44%
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 10 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. a. The probability that the combined sample will test positive is b. Is it unlikely for such a combined sample to test positive?
a. 0.049 b. It is unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is less than or equal to than 0.05.
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 39% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage. b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed. c. Is that probability high enough for the hospital? Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. 0.39x0.39= .1521 b. 1- .1521= .8479 c. No, because it fails 15% of the time
Multiple-choice questions each have four possible answers left parenthesis a comma b comma c comma d right parenthesis, one of which is correct. Assume that you guess the answers to three such questions. a. P(CWW)= b. Beginning with CWW, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list. P(WWC) P(WCW) c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?
a. 1 correct answer out of 4.... .1/4x3/4x3/4= = 9/64 b. 9/64 for both c. (9/64)+(9/64)=(9/64) =27/64
A survey showed that 73% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. a. If 18 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. b. Is 1 a significantly low number of adults requiring eyesight correction?
a. = 2.888e-9 = 9 zeros. SO MOVE THE DECIMAL PLACE TO THE LEFT 9 TIMES = .000 b. yes, it is small (less than 0.05)
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 12.8% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? b. If the student has two such alarm clocks, what is the probability Among 6234 cases of heart pacemaker malfunctions, 335 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 6234 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?that they both fail on the morning of an important final exam? c. What is the probability of not being awakened if the student uses three independent alarm clocks?
a. convert percentage to probability 12.8/ 100= .128 b. multiply it by itself. .128x.128= .016384 c. multiply it again = .00210
For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are a. significantly high (or at least 2 standard deviations above the mean). b. significantly low (or at least 2 standard deviations below the mean). c. not significant (or less than 2 standard deviations away from the mean).
a. statcrunch= greater than or equal to 2= 2.28 b. statcrunch= less than or equal to -2= 2.28 (NO POSITIVE %'s) c. add 2.28+2.28-100= 95.44%
A modified roulette wheel has 32 slots. One slot is 0, another is 00, and the others are numbered 1 through 30, respectively. You are placing a bet that the outcome is an even number. (In roulette, 0 and 00 are neither odd nor even.) a. What is your probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an even number, the payoff odds are 1:1. How much profit do you make if you bet $11 and win? d. How much profit should you make on the $11 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning?
a.= 15/32 b. 17:15 (subtract 32-15) c. 1/1= 1x 11= $11 d. 17:15 ---> 17/15 x11= $12.47
When using the _______ always be careful to avoid double-counting outcomes.
addition
Which word is associated with multiplication when computing probabilities?
and
In a probability histogram, there is a correspondence between _______.
area and probability
Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can a nonstandard normal distribution be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of getting a digit less than 3? a. A nonstandard normal distribtution _______ be used because randomly generated digits have a ______ distribution meaning that each number is _________ to be chosen. b. The probability of getting a digit less than 3 is
cannot, uniform, equally likely The probability of getting a digit less than 3 is 0.3 because less than 3 are digits: 2,1,0 which is 3 numbers out of 10. So, 3/10= 0.3
A _______ is any event combining two or more simple events.
compound
normal probability distributions use ______ data
continuous
Sampling without replacements. Selections are _______ events.
dependent
The _______ of a discrete random variable represents the mean value of the outcomes.
expected value
The _______ (!) denotes the product of decreasing positive whole numbers.
factorial symbol (Ex= 4!= 4x3x2x1 = 24) By special def, 0!= 1.)
Sampling with replacement. Selections are ______ events.
independent
Selections made with replacement are considered to be _______.
independent
Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
independent
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z equals StartFraction left parenthesis x minus mu right parenthesis Over sigma?
mean=0, standard dev=1
Based on a survey, assume that 43% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
n= 6 x= 2 p= .43 q= .57
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 44 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
n=44 p=0.02 less than or equal to 3 P(x) =.9885 and they'll accept 98.85% and reject 1.15%
The probability of any event that is more than .05 is ___________.
not unusual
Formula for calculating mean of a binomial distribution
np
n the binomial probability formula, the variable x represents the
number of successes
A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
random
The _______ states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), we conclude that the assumption is probably not correct.
rare event rule for inferential statistics
In a sample mean distribution, how do you find the mean?
same mean as original distribution because it's the center of the data.
Formula for standard deviation in a binomial distribution
square root of npq
What is the sampling distribution of sample means?
the distribution of all possible sample means, with all samples having the same sample size n taken from the same population.
The expression za denotes the z score with an area of a to its ________.
to its right (a= right, -a=left)
A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 199 lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 lb. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is _____lb.
total/ amount of passengers 3750/25= 150
A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______.
tree diagram
A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.
uniform
The probability of any event that is less than .05 is _________.
unusually high or low unusual