5.1
The probability of an impossible event is ______
The probability of a certain event is ________
The probability that you win a certain raffle is 12%. The probability that you will not with the raffle is __________
The probability of an impossible event is 0 or 0%
The probability of a certain event is 1 or 100%
The probability that you win a certain raffle is 12%. The probability that you will not with the raffle is 88%
The prevalence of a rare disease in the United States is about .01%. The population of the United States is about 230 million. About how many people have this disease?
Which of the following sets has a higher standard deviation?
Set A = {20, 20, 21, 22} Set B = {30, 36, 38, 45}
Note: You do not need to calculate the standard deviation.
If a set of data is normally distributed, then about _______________ of the data lie within one standard deviation below the mean.
If a set of data is normally distributed, then about 68% of the data lie within one standard deviation below the mean.
The _______________ of a poll tells the percentage of such polls in which the confidence interval includes the true result.
The confidence level of a poll tells the percentage of such polls in which the confidence interval includes the true result.
Michael and Surrey are planning to have three children. Assuming it is equally likely for a boy or a girl to be born, what is the probability of having two boys?
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3/8
1. _______________ is the probability that a person who tests negative for a condition does not, in fact, have the condition.
2. _______________ is the probability that a person who does not have a condition actually tests negative for that condition.
1. NPV is the probability that a person who tests negative for a condition does not, in fact, have the condition.
2. Specificity is the probability that a person who does not have a condition actually tests negative for that condition.
Approximately how many data points lie between the minimum and the Third Quartile?
Answer: 75%
The five-number summary splits the data into quarters.
Approximately 25% of the data lies between the minimum and the First Quartile
Approximately 25% of the data lies between the First Quartile and the median
Approximately 25% of the data lies between the median and the Third Quartile.
The average yearly high temperature in a certain city is recorded. It is found that the mean temperature is 70.2°F with a standard deviation of 8.2°F. Assuming that the data are normally distributed, in what range should 95% of the data lie?
70.2 - 2X8.2 = 53.8
70.2 + 2X8.2 = 86.6
Answer: 53.8°F – 86.6°F
According to a Pew Research Center Poll conducted in 2015, 45% of American adults have tablet computers. Suppose the margin of error for a 95% confidence interval is 2.6%. What is the confidence interval for the poll?
45% + 2.6% = 47.6%
The confidence interval is 42.4% to 47.6%.
Suppose you pick a marble from a box containing five red and seven blue marbles. You record the color and put the marble back in the box. What is the probability of getting a red marble both times if you do this twice?
The accompanying table gives the results of a screening test for a disease.
Has disease Does not have disease
Test positive 12 17
Test negative 8 63
Estimate the sensitivity and specificity of the test.
Sensitivity = 12/20 = .6 = 60%
Specificity = 63/80 = 78.75%
The data set below represents the results the grades for a small class on a MTHM 158 exam.
55, 65, 70, 70, 72, 74, 81, 90, 96
Find the five-number summary for the data set.
Q1 = 62.5
Median = 72
Q3 = 85.5
Max = 96
The z-score can be used to compare the relative location of values from the sets of data with different distribution. Suppose that a Statistics class gave two midterms so far. If you scored 76 on Midterm 1 and 78 on Midterm 2, which score is relatively higher than the other? Use the information below.
Midterm 1 Midterm 2
Mean 78 81
Standard Deviation 10 14
Midterm 1: z=(76-78)/10=-.2
Midterm 2: z=(77-81)/14=-.29
Your score on midterm 1 is relatively higher than your score on midterm 2.
According to a Pew Research Center Poll conducted in 2015, 14% of American adults own a portable gaming device. Suppose the confidence interval for a 95% confidence level is 10% to 18%.
1. Can we assert with confidence that at the time of this polling at least 9% of American adults have a portable gaming device? Explain.
2. Can we be absolutely certain that at the time of this polling at least 9% of American adults have a portable gaming device? Explain.
1. YES! The entire confidence interval is above 9% so we are confident at least 9% of American adults have a portable gaming device.
2. NO! The confidence level is only 95%. So, 5% of such samples will produce confidence intervals that will not capture the true value!!!!
To be absolutely certain, we would need to poll the entire population of American adults.
The probability of winning the first is 4% and the probability of winning the second is 2%. There is a small probability of .1% of actually winning both!
Find the probability of winning at least one of the raffles.
The accompanying table gives the results of a screening test for a disease.
Has disease Does not have disease
Test positive 120 170
Test negative 80 630
What is the probability that a person has the disease if he or she tests positive?
You are finding the PPV
PPV = 120/(120+170) = .41379 = 41.4%
Personal Days Used per year by LCCC faculty in 2017:
20 faculty members used 0 personal days
38 faculty members used 1 personal day
42 faculty members used 2 personal days
11 faculty members used 3 personal days.
What is the median number of personal days used by LCCC faculty?
The median number of personal days used by LCCC faculty is “1”.
Assume we know that 20% of Americans suffer from a certain type of allergy. Suppose we take a random sample of 8000 Americans and record the percentage who suffer from this allergy. What guarantees that percentages from such a survey will be normally distributed?
Find the mean and standard deviation of that normal distribution. Round the standard deviation to two decimal places.
1. The central limit theorem
2. The mean is 20%
3. The standard deviation is
√((p(100-p))/n)=√((20(100-20))/8000)=.45
If we conduct a poll of 1300 people, then what is the approximate margin of error for a 95% confidence interval?
margin of error = 100/√n
= 2.77%
Suppose we toss a pair of standard six-sided dice. What is the probability that we get a sum of 4 or below?
6/36 = 1/6 = 16.7%
If you make a matrix with the outcomes of one die going down and the outcomes of the other die going left to right, you will note that there are 36 equally likely outcomes.Of those 36 equally likely outcomes, 6 have a sum of four or below: 1+1, 1+2, 2+1, 1+3, 2+2, 3+1
If 20,000 people in a certain population have the disease, about how many would test positive? About how many would test negative?
90% of 20,000 = 18,000 test positive
10% of 20,000 = 2,000 test negative.
Personal Days Used per year by LCCC faculty in 2017:
20 faculty members used 0 personal days
38 faculty members used 1 personal day
42 faculty members used 2 personal days
11 faculty members used 3 personal days
What is the mean number of personal days used by LCCC faculty? Round to one decimal place.
20+38+42+11 = 111
20X0 + 1X38 + 2X42 + 3X11
Divided by 111 = 1.4
A six-year study in a certain country found that birth weights of newborns were normally distributed, with a mean of 3600 grams and a standard deviation of 455 grams. What is the z-score for a newborn weighing 4250 grams? What percentage of newborns in that country weight more than 4250 grams?
z-score = 1.4
z = 1.4 corresponds to the 91.92 percentile
100 – 91.92 = 8.08
8.08% of newborns weigh more than 4250 grams.
A polling organization conducts a poll by making a random survey and is willing to accept a margin of error of 2.5% at a confidence level of 95%. What should the sample size be?
margin of error = 100/√n=
2.5= 100/√n
2.5 √n=100
√n=100/2.5
√n=40
n = 1600