MATH WK5 Binomial Distribution Quiz, workbook, & exam

Typically, in the middle stages of a country's transition from an emerging nation to a developed nation, death rates fall while birth rates fall. What type of covariance do death rates and birth rates have?

+ covariance

If five students take Exam 1 and score 81, 85, 89, 93, and 97 and five students take Exam 2 and score 83, 89, 91, 92, 95, which test has more variance? If five students take Exam 1 and score 81, 85, 89, 93, and 97 and five students take Exam 2 and score 83, 83, 84, 95, 96, which test has more variance?

- Exam 1 - Exam 2

As gas prices increase, people avoid using their car and are more likely to carpool, which reduces their driver miles. Gas prices and driver-miles exhibit what type of covariance? Every 365 days the earth orbits the sun, producing four seasons. Every 27 days, the moon orbits the earth, producing different phases. What is the covariance between the phase of the moon and the season?

- Negative covariance (Since gas prices and driver miles move together, but in opposite directions, they exhibit negative covariance) - No Covariance

The weather in Seattle has no impact on the weather in Los Angeles. What type of covariance do Seattle and Los Angeles exhibit? When people are watching Netfix, HBO viewership goes down. What type of covariance is there between Netfix and HBO viewership?

- No Covariance - Negative Covariance

If Apple and Microsoft tend to move in the same direction, what type of covariance do they exhibit? If the stock prices of Ford Motors and General Motors both fell during the recession, what type of covariance did they exhibit?

- Positive Covariance - Positive covariance

How would you describe a density curve with a long tail to the right? Which characteristics describe a normal curve? In a distribution that is skewed to the right, which is accurate? In a distribution that is skewed to the left, which is accurate?

- Right Skewed - The mean and median are equal. - The mean is greater than the median. - The median is greater than the mean.

When using the Central Limit Theorem, having a sufficiently large sample size refers to: When applying the Central Limit Theorem to a skewed distribution, the means of each sample will form a:

- The number of members in each sample. - Normal Distribution

If normal distribution A has a wider base than normal distribution B, which of the following is true? If normal distribution X has a taller peak than normal distribution Y, which of the following is true?

- The variance of A is larger than the variance of B. - The variance of Y is larger than the variance of X.

What is the sum of all of the values under a normal distribution equal to?

1

If the average height of a female in the U.S. is 65 inches and the standard deviation of female heights is 2.5 inches, what is the probability that a randomly selected female will be between 60 and 62.5 inches? (Assume a normal distribution.)

14%

Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Danny scores two standard deviations below the mean, what percentile is he?

2.5th

If a six-sided die is rolled three times, how many possible outcomes are there?

216 (6*6*6)

If the average height of a male in the U.S. is 70 inches and the standard deviation of male heights is 3 inches, what is the probability that a randomly selected male will be between 70 and 73 inches? (Assume a normal distribution.)

34%

Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Sarah scores at the median, what percentile is she?

50th

If 500 students take the same exam, and the results form a normal distribution, what is the probability that a randomly chosen student is within one standard deviation of the mean?

68%

.Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Tara scores one standard deviation above the mean, what percentile is she?

84th

If 500 students take the same exam, and the results form a normal distribution, what is the probability that a randomly chosen student is within three standard deviations of the mean?

99.7%

Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Conrad scores three standard deviations above the mean, what percentile is he?

99.7th

If five students take Exam 2 and score 83, 83, 84, 94, 96, what is the standard deviation of Exam 2? (Round your answer to the nearest whole number.)

Calculate the variance of Exam 2 by going through each of the four steps: Determine that the average score is 88 Determine that the differences between each score and the mean are -5, -5, -4, 6, 8 Square all of the differences to get 25, 25, 16, 36, 64 Take the average of the squared differences to get 33.2 The standard deviation on Exam 2 is equal to the square root of the variance Take the square root of the variance to get 5.76 Round to the nearest whole number to get 6 Answer: 6

If five students take Exam 1 and score 81, 85, 89, 93, and 97, what is the variance on Exam 1?

Determine that the average score is 89 Determine that the differences between each score and the mean are -8, -4, 0, 4, 8 Square all of the differences to get 64, 16, 0, 16, 64 Take the average of the squared differences to get 32 Answer: 32

If a die is rolled three times, what is missing to make this a binomial random variable?

Each trial needs to have two possible outcomes, a success and a failure.

If a gambler rolls four dice and wins every time one of the dice shows a 3, what is the frequency of outcomes that the gambler wins on two of the dice?

Four dice are being rolled, and we're expecting two wins. Therefore, use the formula for a combination C(n, k) = n!/k!(n-k)! and replace n with 4 and k with 2 to get C(4, 2) = .4!/2!(4-2 )! Simplify the fraction to get 6. Therefore, there are 6 outcomes with two wins (i.e., WWLL, WLWL, WLLW, LWWL, LWLW, LLWW).

Normal distributions are defined by which two of the following?

Mean and standard deviation

If a company's profits increase when the economy slows, what type of covariance is there between this company and the broader economy?

Neg. Covariance

Typically, in the early stages of a country's transition from an emerging nation to a developed nation, death rates fall while birth rates stay constant. What type of covariance do death rates and birth rates have?

No Covariance

Typically, in the late stages of a country's transition from an emerging nation to a developed nation, death rates stay constant while birth rates fall. What type of covariance do death rates and birth rates have?

No Covariance

If 10 students take the same exam, and the results do not form a normal distribution, what is the probability that a randomly chosen student is within one standard deviation of the mean?

No way to know. Not enough info

Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Charlie scores at the mean, what percentile is he?

Not enough info to determine

If 500 students take the same exam, and the results form a normal distribution, what is the probability that a randomly chosen student is within one standard deviation above the mean?

The distribution is normal, so apply the Empirical Rule The Empirical Rule states that 68% of results are within one standard deviation of the mean 68% includes one standard deviation above or below the mean, so divide 68% by 2 to narrow the range to just students who are above the mean Answer: 34%

If 500 students take the same exam, and the results form a normal distribution, what is the probability that a randomly chosen student is between two and three standard deviations above the mean?

The distribution is normal, so apply the Empirical Rule The Empirical Rule states that 95% of results are within two standard deviation of the mean and 99.7% of results are within three standard deviations of the mean Therefore, 4.7% (99.7% - 95%) of students are between two and three standard deviations from the mean 4.7% includes both sides of the mean, so divide 4.7% by two to narrow the range to just students above the mean 4.7% divided by 2 equals 2.35%, which can be rounded to the nearest percent to get 2% Answer: 2%

If 500 students take the same exam, and the results form a normal distribution, what is the probability that a randomly chosen student is within two standard deviations below the mean?

The distribution is normal, so apply the Empirical Rule The Empirical Rule states that 95% of results are within two standard deviations of the mean 95% includes one standard deviation above or below the mean, so divide 95% by 2 to narrow the range to just students who are below the mean 95% divided by 2 equals 47.5%, and 47.5% rounded to the nearest percent is 48% Answer: 48%

If instead of scoring 83 on Exam 2 (83, 83, 84, 94, 96), one of the students scored 85, how will that affect the mean and standard deviation of Exam 2?

The mean will increase, but the standard deviation will decrease.

If four cards are drawn from a deck with a success measured by drawing a king, what is missing to make this a binomial random variable?

The trials need to be independent of each other.

A gambler rolls two six-sided dice with a goal of getting 6 on both dice. How many possible outcomes are there?

There are 6 outcomes for each die, and 2 dice are being rolled. Therefore, raise 6 to the second power to get 6, which can be simplified to get 36.

If a gambler rolls four dice and wins every time one of the dice shows a 3, what is the probability that the gambler wins on any given die? (Give your answer as a decimal rounded to two decimal places.)

There are 6 sides to each die, and 1 of those sides has a winning three. Therefore, there is a 1/6 , or 0.17, probability of winning.

If five students take Exam 1 and score in the range of 81 to 97 and 5 student take Exam 2 and score in the range of 83 to 95, which test has more variance?

There is not enough info to tell

Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Ian scores at the mean, can we determine what percentile he is?

no