STATISTICS -

Part 1 of 9 -

Suppose that a histogram of a data set is approximately symmetric and "bell shaped". Approximately, what percent of the observations are within three standard deviations of the mean?

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Part 2 of 9 -

If the probability that it will rain tomorrow is 0.38, then the probability that it will not rain tomorrow is:

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What is the probability of drawing two queens in a row from a standard deck of cards without replacement?

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Part 3 of 9 -

Find the variance of the following probability distribution. 

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According to an Internet posting, 80% of adults enjoy drinking beer. A group of 7 adults is chosen randomly. The probability that no more than 3 of them enjoy drinking beer is:

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The probability distribution associated with the number of cartoons watched by Mrs. Kelly's first grade class on Saturday morning is shown below. 

      x P(X)

0 0.15

1 0.20

2 0.30

3 0.10

4 0.20

5 0.05

0

Find the standard deviation for the probability distribution above.

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Part 4 of 9 -

One reason for standardizing random variables is to measure variables with:

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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.

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The standard deviation of a probability distribution must be:

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The continuous distribution characterized by a symmetric, bell-shaped curve is the:

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Given that Z is a standard normal variable, the value z for which P(Z < z) = 0.2580 is

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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

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Part 5 of 9 -

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 between 10 and 30? Place your answer in the blank. Do not use any stray symbols.  For example, 123 would be a legitimate answer.  

Part 6 of 9 -

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.  It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph? Place your answer, rounded to four decimal places, in the space.  

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 non-assigned 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. 

Part 7 of 9 -

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 president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. What is the probability that at least two of the three vice presidents can attend the meeting? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 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.  A particular brand of women's jeans is available in seven different sizes, three different colors, and three different styles. How many different jeans does the store manager need to order to have one pair of each type of jean? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.  

Part 8 of 9 -

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 are the two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry.  Lower value   Upper value  

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 are the two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry.  Lower value   Upper value  

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.  Only 5% of the students taking the test scored higher than what value? Place your answer, rounded to a whole number, in the blank. For example, 78 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.  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 higher than 71 on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 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.  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.  

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 $20 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.  

Part 9 of 9 -

Using the standard normal curve, the Z- score representing the 99th percentile is 2.326.

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The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.

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