Question 1
Given the following boxplot where m is the median value, what statement could be made about the distribution of the data?
A.The distribution is positively skewed.
B.The distribution is negatively skewed.
C.The distribution is approximately symmetric.
D.No statement can be made about the data because no data values are shown on the plot.
Question 2:
P(A) = 1 - p(A)is the:
A.rule of complements
B.addition rule
C.rule of opposites
D.commutative rule
Question 3:
A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?
A.0.0264
B.0.0531
C.0.0347
D.0.0482
Question 4:
If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game?
A.$3.06
B.-$2.78
C.-$3.06
D.$2.78
Question 5:
A researcher surveyed college students to study their opinion about the proposed change in smoking rules. The researcher asked a group of 30 students: 12 of them supported the change, 13 of them did not, and 5 had no opinion. This is not a binomial model because...
A....there are 3 possible outcomes, not 2.
B....the students who strongly supported the change and those who only mildly supported the change are counted the same.
C....less than half of the students supported the change.
D.30 students are not enough for a good sample
Question 6:
Find the variance of the following probability distribution.
| X |
P(X) |
| 1 |
0.20
|
| 2 |
0.15
|
| 3 |
0.25
|
| 4 |
0.25
|
| 5 |
0.15
|
A.1.34
B.1.8
C.0.48
D.1.16
Question 7:
The average height of flowering cherry trees in a nursery is 11 feet. If the heights are normally distributed with a standard deviation of 1.6, find the probability that a randomly selected cherry tree in this nursery is less than 13 feet tall.
A. 0.67
B.0.89
C.0.95
D.0.11
Question 8:
The normal distribution is:
A.the single most important distribution in statistics
B.a density function of a discrete random variable
C.a binomial distribution with only one parameter
D.a discrete distribution
Question 9:
The standard deviation of a probability distribution must be:
A.less than the value of the mean
B.a number between 0 and 1
C.a negative number
D.a nonnegative number
Question 10:
The standard normal distribution has a mean of and standard deviation of, respectively.
A.1 and 0
B.1 and 1
C.0 and 0
D.0 and 1
Question 11:
The standard deviation of X. is usually called the
A.standard error of the mean
B.randomized standard error
C.standard error of the sample
D.standard error of the population
Question 12:
Given that Z is a standard normal variable, the value z for which P(Z < z) = 0.2580 is
A.-0.70
B.0.242
C.0.758
D.-0.65
Question 13:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The histogram below represents scores achieved by 250 job applicants on a personality profile.
How many job applicants scored below 60? Place your answer in the blank. Do not use any stray symbols. For example, 123 would be a legitimate answer.
Question 14:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas (1+i) is not. {0+9i} is valid whereas {9i} is not.
A school determines that the number of children X in the families who attend the school follows the distribution below:
|
Number of children X
|
1
|
2
|
3
|
4
|
5
|
|
Probability P(X)
|
0.20 |
0.35
|
0.25
|
0.15
|
0.05
|
What is the mean number of children per family? Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry.
Question 15:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas (1+i) is not. (0+9i) is valid whereas {9i} is not.
The annual returns, in percentages, on stocks A and B for three possible states of the economy are given in the table below.
|
Economy State
|
Probability
|
StockA
|
StockB
|
|
Good
|
0.5
|
40
|
20
|
|
Average
|
0.3
|
20
|
40
|
|
Bad
|
0.2
|
10
|
8
|
If one invested in StockA, what would be the standard deviation of the percentage return? Place your answer, in percent rounded to 1 decimal place, in the blank. For example, a standard deviation of 10.39 percent would be reported as 10.4. Do not use a percent sign.
Question 16:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+11) is valid whereas {1+i} is not. (0+9i) is valid whereas {9i} is not.
An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
Ai = chocolate chosen
A2 = strawberry chosen
A3 = vanilla chosen
B = ice cream on a cone
B = ice cream in a cup
Find the probability that the ice cream was sold on a cone and was strawberry flavor. Place your answer, rounded to 2 decimal places, in the blank. For exampe, 0.34 would be a legitimate entry.
Question 17:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas (1+i) is not. (0+9i) is valid whereas {9i} is not.
A probability experiment has two steps. There are two possible results for the first step, call them "A" and "B". If the result for the first step was "A", then there would be 4 possible results for the second step. If the result for the first step was "B", then there would be 16 possible results for the second step. How many possible outcomes are there for this experiment? Place your answer in the blank. Do not use any decimal point or comma. For example, 45 would be a legitimate entry.
Question 18:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: {1+14 is valid whereas (1+i) is not. {0+9i} is valid whereas {9i} is not.
The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate entry.
Question 19:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: {1+14 is valid whereas (1+i) is not. (0+9i) is valid whereas {9i} is not.
A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.
What is the probability that a randomly selected customer will spend less than $15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.
Question 20
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: {1+14 is valid whereas {1+i} is not. (0+9i) is valid whereas {9i} is not.
Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.
Find probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry.
Question 21:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas {1+i} is not. (0+9i) is valid whereas {9i} is not.
The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.
Question 22:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas (1+i) is not. (0+9i) is valid whereas {9i} is not.
Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of "C" to students scoring between the 60th and 70th percentiles on the exam.
What score represents the 60th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.
Question 23:
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: (1+1i) is valid whereas {1+i} is not. (0+9i) is valid whereas {9i} is not.
A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.
What is the probability of getting a score between 65 and 89 on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.
Question 24:
A random variable X is normally distributed with a mean of 100 and a variance of 25. Given that X = 110, its corresponding Z- score is 0.40.
True
False
Question 25:
Using the standard normal curve, the Z- score representing the 99th percentile is 2.326.
True
False