Statistic Midterm
Find the indicated area. Find the area of the indicated region under the standard normal curve.
(-1.83 0.55) = 0.6752 (-0.5 2 ) = 0.6687 (-1 1.5 ) = 0.7445
Find the indicated probability. The age of professors at a certain university is normally distributed with an average of 45.0 years and a standard deviation of 6.0 years. If 16 professors are chosen at random for a committee, find the probability that the average age of those professors is less than 42.0 years.
0.0314
Determine the following probability. If the probability of being put on hold while trying to call the IRS is 0.81, then the probability you will not be put on hold is:
0.19
Find the indicated probability. Sixty percent of clowns aren't funny. If you randomly encounter three different clowns, what is the probability that none of them are funny?
0.216
Determine the number of standard deviations from the mean (z-score). In the United States, the distribution of a male's height has a mean of 69 inches with a standard deviation of 3 inches. How many standard deviations from the mean is John Doe, who is 65 inches tall?
1.33 standard deviations below the mean
Determine the number of standard deviations from the mean (z-score).In the United States, the distribution of a female's height has a mean of 64 inches with a standard deviation of 3 inches. How many standard deviations from the mean is Sally, who is 69 inches tall?
1.67 standard deviations above the mean
Find the Indicated Probability. A survey of 150 people revealed that 115 people like ketchup on their hot dogs, 85 people like mustard on their hot dogs and 60 people like both. What proportion of those surveyed like ketchup or mustard on their hot dog?
140/150
The following histogram represents the distribution of Heights of 31 Black Cherry Trees. Approximately what percent of the Cherry trees are less than 70 feet tall? 19 %
19 %
Find the indicated probability. A large basket of fruit contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana?
4/5
Find the indicated probability. On a particular night, a baseball stadium sells 60% of its seats, and of those, 15% do not end up showing up to the game. Assuming everyone present is sitting in a seat, what percentage of seats in the stadium are empty?
49%
Find the indicated probability.At a certain college 40% of the students are male, and of those, 15% smoke cigarettes. What is the percentage of the student body who are male smokers?
6%
Use the graphical display to answer the question. The following box-plot contains the cholesterol levels of 100 patients. How many of the patients had cholesterol levels between 154 and 211? 75
75
Use the graphical display to answer the question. The following box-plot contains the cholesterol levels of 100 patients. How many of the patients had cholesterol levels between 180 and 265?
75
Identify the sampling method used. A manufacturing company is interested in how a new sick-leave policy affects the number of days its employees miss per year. They decide to implement the new policy with one randomly selected manufacturing facility out of the 7 manufacturing facilities they have across the nation and analyze the results to determine effectiveness. What type of sampling method is being used?
Cluster Sample
The temperature of a freshly brewed cup of coffee. Is
Continuous
The wind speed recorded at Tampa International Airport is
Contonuous
The number of hot dogs sold during a game by a Tampa Bay Ray hot dog vendor. Is
Discrete
The number of oranges contained in a 5-pound bag is
Discrete
Find the indicated probability.In general, the probability that a blood donor has Type A blood is 0.40.Consider 8 randomly chosen blood donors, what is the probability that exactly half of them have Type A blood.
Exactly half of them have type A is 0.2322 more than half of them have Type A is 0.1737
Use z-scores to make the following comparison.. Assume that male and female heights are normally distributed and that the average height for a male is 71 inches with a standard deviation of 4.3 inches and that the average height for a female is 65 inches with a standard deviation of 3.5 inches.Determine whether a male who is 82 inches tall or a female who is 77 inches tall is comparably taller after the variable gender has been accounted for. FEMALE
FEMALE
The median graduation rate among the 16 Pinellas County high schools is reported to be 75%. This means that:
Half of the 16 high school have a graduation rate at or below 75%
A study of high school dropout rates in all 50 states reported a median dropout rate of 25%. Interpret this result. Half of the 50 states had a dropout rate at or below 25%.
Half of the 50 states had a dropout rate ar or below 25%
. The type of marsh found growing in a reserve.
Qualitative
The length of a super bowl commercial
Quantitative
Use z-scores to make the following comparison. A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of Assuming the performance on both tests follows a normal distribution, determine which test the student did better on?
SAT
Identify the overall shape of the distribution and determine whether the mean or the median would provide a better measure of center. Shown below is a histogram for the height of 51 students.
Skew left, the median would provide a better measure of center
Identify the overall shape of the distribution and determine whether the mean or the median would provide a better measure of center. Shown below is a histogram for the length of 50 iTunes songs
Skew right, the median would provide a better measure of the center.
Find the indicated probability. A hotel has 20 rooms on the first floor, 60 rooms on the second floor, 40 rooms on the third floor, and 20 rooms on the fourth floor. If a hotel room is assigned at random, what is the probability of getting a room on an odd floor?
if is and odd floor is 3/7 if is even is 4/7
Determine the following probability. The probability of an individual having Type A blood is 0.40. What is the probability of an individual having a blood type other than A?
0.60
Determine the following probability. The probability of an individual having Type O blood is 0.45. What is the probability of having a blood type other than O?
0.55
Determine the number of standard deviations from the mean (z-score). In the United States, the distribution of a male's height has a mean of 69 inches with a standard deviation of 3 inches. How many standard deviations from the mean is John Doe, who is 67 inches tall?
0.67 standard deviations below the mean.
IQ scores are known to be normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly selected individual has an IQ score that is less than 120?
0.9082
Use z-scores to make the following comparison. A high school student took two college entrance exams, scoring 1110 on the SAT and 27 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 130 while the ACT scores have a mean of 22 and a standard deviation of Assuming the performance on both tests follows a normal distribution, determine which test the student did better on? .
ACT
Determine the probability. The deck of cards in Candy Land has 48 single-move cards, 12 double-move cards, and 6-character cards. If a card is drawn at random, what is the probability it is a character card?
If is a character card is 1/11 IF is a double moved card is 2/11
Find the indicated probability. Empirical evidence shows that the "normal" resting adult body temperature is normally distributed with a mean of 98.2 degrees Fahrenheit and a standard deviation of 0.7 degrees Fahrenheit. What is the probability that a randomly selected adult has a "normal" resting body temperature that is greater than 99 degrees Fahrenheit? 0.13
If is greater than 99 degrees fahrenheit is 0.13 If the temperature is between 98-99 is 0.4870
Determine the probability. At a certain college, there are 600 freshman, 400 sophomores, 300 juniors, and 200 seniors. If one student is selected at random, what is the probability that the student is a sophomore?
Is is sophomore is 4/15
Identify the sampling method used. A quality control department for a manufacturing facility thoroughly inspects every 50thitem produced to ensure that it meets quality standards.
Systematic Sample
Identify the sampling method used. A quality control department for a manufacturing facility thoroughly inspects every 50thitem produced to ensure that it meets quality standards is?
Systematic Sample.
Find the mean. The following data set contains 6 quiz scores coming from a class of 30 students. 13 8 13 8 4 8. The mean is 9
The mean is 9
Select the most appropriate response.A company maintains a fleet of vehicles that consist of both cars and trucks. The miles per gallon realized in the cars follows a normal distribution with mean of 30 and a standard deviation of 2 while the miles per gallon realized in the trucks follows a normal distribution with mean of 17 with a standard deviation of 3. Which distribution is more variable?
The mpg for the trucks
Find the range. An academic adviser recorded the number of classes six randomly selected students were enrolled in. 4 4 1 2 3 5.
The range is 4
Determine the range. The following data set contains 6 quiz scores from a class of 30 students .13 8 13 8 4 8, the range is 9
The range is 9
Identify the Population. A study is conducted to determine the average amount of money full-time SPC students spend on textbooks per semester. A sample of 100 full-time SPC students is taken by dividing the student body into freshmen, sophomores, juniors and seniors, and then selecting a proportional number from each class. Each student in the sample is asked how much money he/she spent on books for the current semester:
The set of all full-time SPC students
Find the sample standard deviation. An academic adviser recorded the number of classes six randomly selected students were enrolled in. 4 3 1 2 3 5,
The standard deviation is 1.41
All human blood can be "ABO" typed as belonging to one of A, B, O, or AB types. The actual distribution varies slightly among different groups of people, but for a randomly chosen person from North America, the following are the approximate probabilities: What is the probability that a randomly chosen person from North America has AB type blood?
0.04
Find the indicated probability. Let X be the number showing on a fair six-sided die. The distribution of X has mean 3.5 and standard deviation 1.71. If a six-sided die is rolled 30 times, what is the probability that the average of all 30 rolls is less than 3?
0.0548
A baseball park has determined that the number of people contained in each vehicle parked in one of their lots has following distribution. What is the probability that more than 4 people arrive in a vehicle?
0.10
Find the indicated probability.Recent statistics show that 62% of people wash their hands after using the restroom. If you shake hands with three random people, what is the probability that all of them washed their hands after previously using the restroom?
0.2383
In the United States, the distribution of a female's height has a mean of 64 inches with a standard deviation of 3 inches. How many standard deviations from the mean is Sally, who is 65 inches tall?
0.33 standard deviations above the mean
Determine the following probability. At a certain middle school, 3 out of 5 students make the honor roll. What is the probability that a student does not make the honor roll?
0.40
Find the indicated probability.IQ scores are known to be normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly selected individual has an IQ score that is between 100 and 120?
0.4082
Find the indicated probability.The age of professors at a certain university is normally distributed with an average of 45.0 years and a standard deviation of 6.0 years. If 16 professors are chosen at random for a committee, find the probability that the average age of those professors is greater than 42.0 years.
0.9772
Identify the score corresponding to the indicated percentile. Cardiac pacemaker batteries will stop working if they are not properly calibrated and charged. Suppose that the length of time a battery operates follows a normal distribution with mean 25.0 days and standard deviation 2.0 days. At what point will 1% of the batteries will fail?
20.34 days
Identify the z-score corresponding to the indicated percentile. For the standard normal curve, identify the z-score that corresponds to the 20th percentile. -0.84
20th percentile is -0.84 67th percentile is 33th percentile is -0.44 80th percentile is 0.84
The following histogram represents the distribution of Heights of 31 Black Cherry Trees. Approximately what percent of the Cherry trees are greater than 80 feet tall?
23%
Identify the score corresponding to the indicated percentile. The length of human pregnancies (with no complications) from conception to birth varies according to a normal distribution with mean 260 days and standard deviation 10. Only ten-percent of pregnancy lengths are less than what value?
247 days
Find the Indicated ProbabilityIn. The US, 37% of household have dogs, 30% of households have cats, and 7% of households have both cats and dogs.What percentage of US households have a cat or a dog?
60%
Identify the data value corresponding to the indicated percentile. The heights of women are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. The tallest 10% of females are taller than what height.
68.2 inches
Identify the data value corresponding to the indicated percentile. The amount of sleep an adult gets per day is normally distributed with a mean of 7 hours and a standard deviation of 1.5 hours. Five-percent of adults sleep more than how many hours per day? 9.5 hours
9.5 hours
Use the Empirical Rule (68-95-99.7) to answer the question. A new shingle being used by a roofing company has a normal distribution with an average lifetime of 17-years and a standard deviation of two-years. Approximately what percent of shingles should last between 13 and 21 years?
95 %
Use the Empirical Rule (68-95-99.7) to answer the question. The interest rate for the financing of a used car is on average 9% with a standard deviation of 3%. Assuming that interest rates for used car loans are normally distributed, approximately what percent of loans have an interest rate that is between 3% and 15%? 95 %
95%
Use the Empirical Rule (68-95-99.7) to answer the question. A new shingle being used by a roofing company has a normal distribution with an average lifetime of 17-years and a standard deviation of two-years. Approximately what percent of shingles should last between 11 and 23 years?
99.7 %
Use z-scores to make the following comparison. Assume that male and female heights are normally distributed and that the average height for a male is 71 inches with a standard deviation of 4.3 inches and that the average height for a female is 65 inches with a standard deviation of 3.5 inches.Determine whether a male who is 82 inches tall or a female who is 77 inches tall is comparably taller after the variable gender has been accounted for.
Female
Find the indicated probability. In general, after a group makes a reservation at a restaurant, they do not show up 20% of the time. If a restaurant has 8 reservations for the evening, what is the probability that exactly two do not show up?
IF exactly two do not show up is 0.2936 IF more than two do not show upis 0.7064
Find the indicated probability. An insurance company has determined that the cost of a certain medical procedure varies according to a normal distribution with a mean of $800 and a standard deviation of $40. If a new insurance claim comes in for this particular medical procedure, what is the probability that the claim will be less than $900?
If the claim is less than 900 is 0.9938 If the claim is greater than 900 is 0.0062
Find the median. An academic adviser recorded the number of classes six randomly selected students were enrolled in. 4 4 1 2 3 5. The median is 3.5
The median is 3.5
Find the median. The following data set contains 6 quiz scores from a class of 30 students. 13 8 13 8 4 8
The median is 8
Find the mode. An academic adviser recorded the number of classes six randomly selected students were enrolled in. 4 4 1 2 3 5
The mode is 4
Select the most appropriate response. One normal distribution has a mean of 34 and a standard deviation of 2 and another normal distribution has a mean of 23 with a standard deviation of 7. Which distribution is more variable?
The second normal distribution
A study is done to determine the average number of semesters a SPC student who is seeking an Associate's Degree takes to complete the degree. In order to obtain a sample, SPC students who are finishing their Associates Degrees are split into full-time and part-time students so that each group can be appropriately represented in the sample. From each of these two groups, the appropriate number of students are randomly selected and the data are recorded.
The set of all SPC students
Find the sample standard deviation. The following data set contains 7 quiz scores from a class of 30 students. 13 8 13 8 4 8 9.
The standard deviation is 3.16
Scores on the verbal reasoning portion of the GRE have a mean of 150 and a standard deviation of 8. What can be said about a particular student's performance if their z-score is negative two? The student scored a 142.
The student scored a 142
The average percentage of correct responses on last semester's Midterm was 78%. What can be said about a particular student's percentage correct if their z-score is positive?
The student scored above 78%
The average percentage of correct responses on last semester's Midterm was 78%. What can be said about a particular student's percentage correct if their z-score is negative?
The student scored below 78%
The blood type of a patient in the emergency room is
qualitative
The elevation of an airport. Is
quantitative
Find the mean. An academic adviser recorded the number of classes six randomly selected students were enrolled in. 4 3 1 2 3 5 R
the mean is 3