Stat Final
Step 1: InvT, (0.2/2, 4-1) = -1.6377 --> 1.6377 *always positive if to the right of mean Step 2: Stat, Test, T-Interval (instead of Z because n is less than 30) (75.89, 13.53, 4, 0.8) = (64.81, 86.97)
A consumer affairs investigator records the repair cost for 44 randomly selected TVs. A sample mean of $75.89 and standard deviation of $13.53 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Step 2 of 2 : Construct the 80% confidence interval.
0.5846 2nd Vars, BinomPDF, 14, 0.1, 1 = 0.35586 2nd Vars, BinomPDF, 14, 0.1, 0 = 0.22877 0.35586 + 0.22877 = 0.5846
A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 11 or less, the lot passes inspection. Suppose 10% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection?
binomPDF (14, 0.4, 12) + binomPDF (14, 0.4, 13) + binomPDF (14, 0.4, 13) - 1 = 0.9994 or binomPDF (14, 0.4, 0) + binomPDF (14, 0.4, 1) + binomPDF (14, 0.4, 2) + binomPDF (14, 0.4, 3) + binomPDF (14, 0.4, 4) + binomPDF (14, 0.4, 5).... etc = 0.9994
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color red. If 14 buyers are randomly selected, what is the probability that less than 12 buyers would prefer red?
68%
A restaurant in Clemson reports that diners spend an average of $ 49.20 during peak hours of operation, with a standard deviation of $ 7.00 . Using the empirical rule, about what percent of diners spend between $ 42.20 and $ 56.20 ?
6 x 6 = 36 (# of possible outcomes) 1/36 + 2/36 + 3/36 + 4/36 + 5/36 + 6/36 + 5/36 + 4/36 = 30/36 = 5/6 or 0.833
A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than or equal to 9?
binompdf (17, 0.2, 4) = 0.2093
A student takes an exam containing 17 multiple choice questions. Each question has 5 choices. If the student guesses, what is the probability that he will get exactly 4 questions right?
standard dev. = (x - mean) / z = (28 - 20.7) / 1.476 = 4.9
ACT scores have a mean of 20.7 and 7 percent of the scores are above 28. The scores have a distribution that is approximately normal. Find the standard deviation.
Quantitative, Discrete, Ratio
Answer whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. The heart beats per minute of 40 randomly selected people. Are these data qualitative or quantitative? Are these data discrete or continuous? Discrete Continuous Neither What is the highest level of measurement the data possesses? Nominal Ordinal Interval Ratio
Some cruise ship passengers choose to wear magnetic bracelets, which they (the passengers) say diminish the effects of motion sickness. The on-ship medical clinic notes the number of passengers wearing bracelets who complain of motion sickness and compares it to the number of passengers not wearing bracelets who complain of motion sickness. Does the above situation describe an observational study or an experiment? Why?
Answer: D
A university dean is interested in determining the proportion of students who receive some sort of financial aid at his school. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. What is the population being studied? a.) The 118 students who recieved financial aid b.) All students in the USA c.) The true proportion of students at the university who received financial aid d.) All of the students at the dean's university
Answer: d.) All of the students at the dean's university
binompdf (6, 0.7. 0) + binompdf (6, 0.7, 1) = 0.0109
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. P(X<2), n=6, p=0.7
Answer: 78
Below is a dataset of the speed of tennis serves (in mph) for women's tennis. If you were to create a boxplot of the data which (if any) of the values would be classified as outliers? 78 95 110 114 116 117 120 120 121 122 128
Quantitative (measures numeric variables, how much, how often)
Boiling points in degrees Celsius for various substances are an example of which type of data? Qualitative Quantitative
Enter data into L1 and L2, putting the midpoint of the data in for L1. Press 1st var stats, and make sure to put L1 into List and L2 into FreqList. Mean: 78.25 Sample Variance: 1st var stats, square Sx (our standard deviation) = 75.5
Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American adults.
z = 33.6 - 32.5 / 6.9 = 0.16
Calculate the standard score of the given x value, x=33.6, where μ=32.5, σ=6.9.
2nd vars, poisson cdf, 6, 5 = 0.4457
Cars enter a car wash at a mean rate of 3 cars per half an hour. What is the probability that, in any hour, no more than 5 cars will enter the car wash?
Continuous
Classify the following as either a discrete random variable or a continuous random variable. The amount of sugar imported by the U.S. in a day.
Discrete
Classify the following as either a discrete random variable or a continuous random variable. The heartbeats per minute of 64 randomly selected people. (Lesson 6)
Continuous
Classify the following as either a discrete random variable or a continuous random variable: The actual volumes in 50 recently manufactured bottles of mineral water.
Discrete- a random variable which has a countable number of possible outcomes. Since there is no such thing as half a complaint, the data in the problem would be discrete.
Classify the following as either a discrete random variable or a continuous random variable: The number of customer complaints received each day.
Qualitative, Neither, Nominal
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. You toss a coin and record "head" as 1 and "tail" as 2. Are these data qualitative or quantitative? Qualitative Quantitative Are these data discrete or continuous? Discrete Continuous Neither What is the highest level of measurement the data possesses? Nominal Ordinal Interval Ratio
To calculate sample variance: 1st var stats, and square Sx
Consider the following data: 12,2,4,2,4,6 Step 1 of 3 : Calculate the value of the sample variance. Round your answer to one decimal place.
Step 1: Determine the mean = -12 -10-(-12) = 2 -14-(-12) = -2 -14-(-12) = -2 etc. = 24 24 / 5 (found from n-1) = 4.8 Step 2: = Square root of variance (4.8) = 2.19 Step 3: = 4
Consider the following data: −10,−14,−14,−10,−10,−14 Step 1 of 3 : Calculate the value of the sample variance. Round your answer to one decimal place. Step 2 of 3 : Calculate the value of the sample standard deviation. Round your answer to one decimal place. Step 3 of 3 : Calculate the value of the range.
9, 11, 11, 13
Create a data set who's mean, median, and mode are equal.
False, because the standard deviation is from an average distance and computed from a square root so cannot be negative.
Decide if the following statement is true or false: It is possible to have a standard deviation of −4 for some data set.
No, because at least one probability is greater than 1 or less than 0.
Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not.
Yes, because the probabilities lie between 0 and 1 and the sum is equal to 1
Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. (Lesson 6)
B.) No b/c the intervals overlap
Determine whether the following data could be represented in a histogram. If not, state your reasoning. a.) Yes b.) No, b/c the intervals overlap c.) No, b/c at least one interval is of intermediate width d.) No, b/c intervals are different widths
Not mutually exclusive, because a college student could be a senior and a mathematics major
Determine whether the following events are mutually exclusive. Choosing a student who is a senior in college or a mathematics major from a nearby university to participate in a research study.
Neither: Qualitative data are neither discrete nor continuous. Discrete: Quantitative data that take on values that are countable, such as 00, 11, and 22, are discrete. Continuous: Quantitative data that can take on any value within some interval are continuous.
Discrete, Continuous, and Neither Data
6(0.2) + 7(0.1) + 8(0.2) + 9(0.2) + 10(0.3) = 8.3
Find the expected value of E(X)
invNorm (0.08, 0, 1, LEFT) = -1.41
Find the value of z such that 0.08 of the area lies to the left of z. Round your answer to two decimal places.
(5)^2 (0.3) + (6)^2 (0.2) + (7^2) (0.1) + (8^2) (0.2) + (9^2) (0.2) = 48.6 5(0.3) + 6(0.2) + 7(0.1) + 8(0.2) + 9(0.2) = Expected value of 6.8 stat, edit, 1st var stats ox = 1.536 --> standard deviation ox ^ 2 = 2.36 --> variance
Find the variance and standard deviation for the given data
Qualitative, Neither, Ordinal
Five people are in a bakery waiting for service. Each person takes a ticket when they enter the bakery in order to determine when they will be served. The person with the lowest ticket number will be served next. Are these data qualitative or quantitative? Qualitative Quantitative Are these data discrete or continuous? Discrete Continuous Neither What is the highest level of measurement the data possesses? Nominal Ordinal Interval Ratio
= -31
Given the sample 4, 18, 17, −3, add one more sample value that will make the mean equal to 1.
c.) Quantitative
Goals scored during a soccer game are an example of which type of data? a.) Qualitative b.) statistic c.) Quantitative d.) Inferential
Answer: C
If the events G and H are mutually exclusive, then which of the following is true?
Continuous
Lengths of time it takes for new light bulbs to burn out are an example of which type of data? Discrete Continuous Neither
Step 1: normalCDF(250, 1E99, 230, 29 Step 2: normalCDF(250, 1E99, 230, 29 / square root of n (7) ) = 0.0344
Let X= the number of large bags of popcorn sold by a movie theater in a day. Suppose X is normally distributed w/ a mean of 230 bags/standard dev. of 29 bags. Step 1: What's the probability that on a single day, the theater will sell more than 250 bags? Step 2: If seven days are randomly selected, what's the probability that the average number of popcorn bags sold per day will be greater than 250?
C.) Neither- Because this is qualitative data
Names of TV shows taped in Los Angeles are an example of which type of data? A.) Discrete B.) Continuous C.) Neither
The EPA monitors the quality of air in every major city in the United States and publishes the Air Quality Index. The index rates the air quality of each city in a given day as: Very Unhealthy Unhealthy Unhealthy for Sensitive Groups Moderate Good What is the level of measurement of the Air Quality Index?
Ordinal
0.3375 (54/160)
Out of 350 applicants for a job, 160 are female and 54 are female and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they are female?
Determine if the numerical value describes a parameter or a statistic. A recent poll of 1864 students showed that the average number of hours they study per week is 4.9
Sample Statistic
Neither
Songs on a band's set list are an example of which type of data? Discrete Continuous Neither
Benji and Mikhail are playing their favorite game. The game involves flipping a coin followed by rolling a die. Assume the coin is fair and the probability of Heads (H) and the probability of Tails (T) are both 1/2.Assume the die is a fair and the probability of rolling any number is 1/6. If the coin comes up heads, Benji rolls a die. If the die comes up even, then Benji wins the round. If the coin comes up tails, Mikhail rolls a die. If the die comes up odd, Mikhail wins the round. In any other situation, the game is a draw. Step 1 of 2: What is the probability that Benji won the game? Step 2 of 2: What is the probability that Benji won the game AND the die roll resulted in a 2?
Step 1: 1/4 Step 2: 1/12
The following data set represents the lengths (in cm) of 16 fish caught in a pond at a campground in a weekend: 5 6 8 9 9 10 10 10 11 12 12 15 19 21 22 27 Step 1 of 2: Find the 70th percentile of the data. Step 2 of 2: Determine the percentile rank for the fish with a length of 11 cm. Enter your answer as a percentage rounded to 2 decimal places if necessary.
Step 1: 15cm Step 2: 56.25 % of fish have a length of 11 cm or less
The mean salary at a local industrial plant is $27,300 with a standard deviation of $5400. The median salary is $26,100 and the 61st percentile is $30,200. Step 1 of 5: Based on the given information, determine if the following statement is true or false. Approximately 61% of the salaries are above $30,200. Step 2 of 5: Based on the given information, determine if the following statement is true or false. Joe's salary of $33,240 is 1.10 standard deviations above the mean. Step 3 of 5: Based on the given information, determine if the following statement is true or false. The percentile rank of $26,100 is 50. Step 4 of 5: Based on the given information, determine if the following statement is true or false. Approximately 11% of the salaries are between $26,100 and $30,200. Step 5 of 5: If Tom's salary has a z-score of 0.7, how much does he earn (in dollars)?
Step 1: False * If greater than or equal to, would be true Step 2: True 5400 x 1.10 + 27,300 = 33,240 Step 3: True Step 4: True Step 5: $31,080 5400 x 0.7 + 27300 = 31,080
Answer: 0..58 or 58%
Suppose 58% of the students in a university are baseball players. Step 1 of 3: If a sample of 681 students is selected, what is the mean of the sampling distribution for the sample proportion? Enter your answer as a decimal rounded to two decimal places.
Answer: 0.0189
Suppose 58% of the students in a university are baseball players. Step 2 of 3: If a sample of 681 students is selected, what is the standard error of the sampling distribution for the sample proportion? Enter your answer as a decimal rounded to four decimal places. You will need this value for the next step.
Answer: 0.94
Suppose 58% of the students in a university are baseball players. Step 3 of 3: If a sample of 681 students is chosen, what is the probability that the sample proportion of baseball players will be greater than 55%
square root of (0.1)(1-0.1) / 238 = 0.0194 invNorm (0.194, 0, 1, LEFT) = -2.06 (our z-score) or 0.06 - 0.1 / 0.0194 normal CDF: (LOWER: -2.06, UPPER: 1E99, 0, 1 = 0.9803
Suppose a large shipment of stereos contained 10% defectives. If a sample of size 238 is selected, what's the probability that the sample proportion will be greater than 6%?
=0.8728
Suppose a large shipment of telephones contained 11% defectives. If a sample of size 318 is selected, what is the probability that the sample proportion will be greater than 9%?
Step 1: 5.5−6.5 / 0.5= -2 and 7.5−6.5 / 0.5 = 2 K=2: At least 1 − 1/2^2 = 3/4 = 75% of the data lies within two standard deviations of the mean. K=3: At least 1− 1/3^2 = 8/9 ≈88.9% of the data lies within three standard deviations of the mean. *K = 2 means 75% of the data lies within 2 standard deviations of the mean = 75%
Suppose that quiz scores in a beginning statistics class have a mean of 6.5 with a standard deviation of 0.50. Using Chebyshev's Theorem, what is the minimum percentage of quiz scores between 5.5 and 7.5?
stat, tests, z-test, (992, 141, 977, 37, < U0) = 0.2588
Suppose the horses in a large stable have a mean weight of 992lbs, and a standard deviation of 141lbs. What is the probability that the mean weight of the sample of horses would be less than 977lbs if 37 horses are sampled at random from the stable?
Answer: B, Median
The Bureau of Labor Statistics (BLS) wants to calculate what the "typical" person earns. A sample of 100,000 adults in the US were randomly chosen and their incomes reported. Which measure would be best to describe the "typical" income? A.) Mean B.) Median C.) Mode D.) Range
The data are quantitative since the IQ score of a student at the local college is a measurement and therefore is numerical. The data are also discrete because IQ scores cannot take on values between 130 and 131. The level of measurement is interval because there is no zero point for IQ scores.
The IQ scores of students at the local college are being measured. What is the highest level of measurement the data possesses?
2nd vars, D, 6.4, 5 = 0.1487
The auto parts department of an automotive dealership sends out a mean of 6.4 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 5?
normalCDF (45, 1E99, 42, 2.7)
The height of hobbits, X, is normally distributed with a mean of 42 in. and a standard dev. of 2.7 in. What's the probability that a randomly selected hobbit is at least 45 inches tall?
0.5990 *Don't know how to get this
The mean cost of a five pound bag of shrimp is 50 dollars with a standard deviation of 8 dollars. If a sample of 56 bags of shrimp is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 0.9 dollars?
Stat, Tests, Z-Test, (46, 7, 47.05, 133, >u0) p = 0.0418
The mean lifetime of a tire is 46 months with a variance of 49. If 133 tires are sampled, what is the probability that the mean of the sample would be greater than 47.05 months?
Discrete
The numbers of languages that various people speak fluently are an example of which type of data? Discrete Continuous Neither
1st: InvNorm (Stat, 3), 99% confidence level means the area will be 0.01 / 2 = (0.005, 0, 1) Z-Score = - 2.575 n = (2.575)^2 (0.22) (1-0.22) / 0.03)^2 = 1265 (Round up to next integer)
The state education commission wants to estimate the fraction of 10th-grade students that have reading skills at or below the 8th-grade level. In an earlier study, the population proportion was estimated to be 0.22. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99% confidence level with an error of at most 0.03?
(198-130) / 30 = 2.2667 *Use the Z table =0.98
Trucks in a delivery fleet travel a mean of 130 miles per day with a standard deviation of 30 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 198 miles in a day.
b.) Qualitative
Types of movies people go to see are an example of which type of data? a.) Quantitative b.) Qualitative c.) Inferential
12/96 x 11/96 = 0.0143
What is the probability that a senior Physics major and then another senior Physics major are chosen at random?
Answer: A
Which of the following is a description for a standard deviation?
Plan A
Which plan had the higher payout long term?
RR, RG, RB, GR, GG, GB, BR, BG, BB
Write out the sample space for the given experiment. Use the letter R to indicate red, G to indicate green, and B to indicate blue. A die shows 3 different colors on it. Give the sample space for the next 2 rolls.