Since the population is always larger than the sample, the population mean:

The binomial probability distribution is used with


We assume that the outcomes of successive trials in a binomial experiment are:


Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. What is the probability that fewer than 25 batteries will last at least 8 hours?

Find the probability, P(Z < 0.17), using the standard normal distribution.


The normal distribution is:


The standard deviation of a probability distribution is a:


Given that Z is a standard normal random variable, P(1.0 < Z < 1.5) is


If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?


Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 < X < 90) is

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. What percentage of the job applicants scored below 60? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitimate answer. [removed] 
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.
If one invested in StockA, what would be the expected annual percentage return? Place your answer, in percent, in the blank. For example, an expected 10 percent return would be recorded as 10. Do not use a percent sign. [removed] 

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 following data were obtained from a survey of college students. The variable X represents the number of nonassigned books read during the past six months.
What is the standard deviation of X? Place your answer, rounded to two decimal places in the blank. For example, 4.56 would be a legitimate entry. [removed] 
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. Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that neither of the questionnaires will be returned? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. [removed] 

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. Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
Number of Vehicles Involved
What proportion of accidents involved more than one vehicle? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. [removed] 
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. In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
Place your answer, rounded to four decimal places, in the blank. [removed] When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry. 

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. [removed] 

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 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 $30 or more at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. [removed] 

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. 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 the probability that the mean of the sample is greater than $460. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate answer.[removed] 

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 length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and standard deviation 2.2 minutes. For a door selected at random, what is the probability the assembly line time will be between 5 and 10 minutes? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer. [removed] 

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. 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. [removed] 
Using the standard normal curve, the Z score representing the 85th percentile is 0.67


The left half under the normal curve is slightly smaller than the right half.

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