Question 1

Find the normal probability using a grapher.
-P(z < 1.5)

Accepted Answer

The probability P(z < 1.5) refers to the area under the standard normal curve to the left of z = 1.5. This value is approximately 0.933, which can be found using a standard normal distribution table or a graphing calculator designed for statistical analysis.

Question 2

Obtain the population standard deviation,σ, for the given data. Assume that the data represent population data. Round
your final answer to one more decimal place than that used for the observations.
-The test scores of 9 students are listed below. 
47 73 74
79 77 73
75 53 43

Accepted Answer

To find the population standard deviation (σ), we first calculate the mean (average) of the data, then use the formula for σ, which involves taking the square root of the average of the squared differences between each data point and the mean. For the given data: Mean = (47 + 73 + 74 + 79 + 77 + 73 + 75 + 53 + 43) / 9 = 66.2. Then, calculate each score's deviation from the mean, square those deviations, average them, and take the square root. Doing this calculation gives a standard deviation of approximately 13.3, rounded to one more decimal place than the observations as instructed.

Question 3

Obtain the population standard deviation,σ, for the given data. Assume that the data represent population data. Round
your final answer to one more decimal place than that used for the observations.
-The normal annual precipitation (in inches) is given below for 8 different U.S. cities. 
19.2 17.8 6.5 13.2
19.6 17.6 9.6 6.8

Accepted Answer

To calculate the population standard deviation (σ), we first find the mean (average) of the data, then subtract the mean from each data point and square the result, sum those squared differences, divide by the number of data points (since this is a population), and finally take the square root of that result. For the given data: Mean = (19.2 + 17.8 + 6.5 + 13.2 + 19.6 + 17.6 + 9.6 + 6.8) / 8 = 111.2 / 8 = 13.9. Then, calculate the squared differences from the mean, sum them, divide by 8, and take the square root. Doing this calculation gives a standard deviation of approximately 5.17, rounded to one more decimal place than the observations.

Question 4

Solve the problem.
-What is the probability that 12 rolls of a die will show exactly three sixes?

Accepted Answer

The answer of Solve the problem.
-What is the probability that...

Question 5

Solve the problem.
-The total distances (in miles) cycled by sixteen athletes in the week prior to a cycling race are shown below. Find the interquartile range.
787 644 820 676
475 603 525 663
568 693 875 501
590 460 562 490

Accepted Answer

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). First, we need to arrange the data in ascending order: 460, 475, 490, 501, 525, 562, 568, 590, 603, 644, 663, 676, 693, 787, 820, 875. With 16 data points, Q1 is the average of the 4th and 5th values (501 and 525), and Q3 is the average of the 12th and 13th values (676 and 693). Q1 = (501 + 525) / 2 = 513, Q3 = (676 + 693) / 2 = 684.5. The IQR = Q3 - Q1 = 684.5 - 513 = 171.5 mi.

Question 6

Solve the problem.
-The test scores of 19 students are listed below. Find the interquartile range.

Accepted Answer

The answer of Solve the problem.
-The test scores of 19...

Question 7

Solve the problem.
-The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 18. Find the standard deviation for the number of seeds germinating in each batch.

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula: √(n * p * (1-p)), where n is the number of trials (seeds), and p is the probability of success (germination). Here, n = 18 and p = 0.7. So, the standard deviation is √(18 * 0.7 * 0.3) = √3.78 ≈ 1.9.

Question 8

Solve the problem.
-The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 3. Find the mean for the number of seeds germinating in each batch.

Accepted Answer

The mean for the number of seeds germinating in each batch can be found by multiplying the probability of a single seed germinating (0.7) by the total number of seeds in a batch (3). Thus, the mean is 0.7 * 3 = 2.1.

Question 9

Find the normal probability using a grapher.
-P(z > -1.25)

Accepted Answer

The probability P(z > -1.25) is equivalent to 1 - P(z < -1.25). Using a standard normal distribution table or calculator, P(z < -1.25) is approximately 0.1056. Therefore, P(z > -1.25) is 1 - 0.1056 = 0.8944, which rounds to 0.894.

Question 10

Solve the problem.
-What is the probability that 15 flips of a coin will show exactly 7 tails?

Accepted Answer

The answer of Solve the problem.
-What is the probability that...

Question 11

Solve the problem.
-You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $42, otherwise you lose $30. What is your expected value for the game?

Accepted Answer

The answer of Solve the problem.
-You are playing a game...

Question 12

Find the normal probability using a grapher.
-P(z < 1.25)

Accepted Answer

The probability P(z < 1.25) refers to the area under the standard normal curve to the left of z = 1.25. Using a standard normal distribution table or a graphing tool, we find that this area is approximately 0.894, which corresponds to 89.4% of the area under the curve.

Question 13

Solve the problem.
-A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Four points are awarded for each correct answer, but the student loses 2 points for an
Incorrect answer. Questions left blank neither receive nor lose points. Is it in the student's best interest to guess?

Accepted Answer

It is not in the student's best interest to guess because the expected value of guessing is negative. With 1 correct answer out of 5 options, the expected gain is 4 points, but the expected loss from 4 incorrect answers is 8 points (4 x -2), resulting in a net loss.

Question 14

Solve the problem.
-The star of the college basketball team has a 70% foul shooting average. If the player attempts 5 foul shots in a game, what is the probability that they will make at least 4 foul shots?

Accepted Answer

The probability of making at least 4 out of 5 shots, with each shot having a 70% chance of success, can be calculated using the binomial probability formula. The probability of making exactly 4 shots is $5 \times (0.7)^4 \times (0.3)^1$, and the probability of making all 5 shots is $(0.7)^5$. Adding these probabilities gives the total probability of making at least 4 shots, which is approximately 0.5282.

Question 15

Obtain the population standard deviation,σ, for the given data. Assume that the data represent population data. Round
your final answer to one more decimal place than that used for the observations.
-The weekly salaries (in dollars) of seven government workers are listed below 
688 744 683 550 502 545 810

Accepted Answer

To find the population standard deviation, first calculate the mean of the data, then find the squared differences from the mean, average those squared differences, and finally take the square root. The correct calculation results in a standard deviation of 106.8.

Question 16

Solve the problem.
-Suppose that there is a lottery that cost $1 to play. You must pick five digits in order from 0 to 9 and duplicates are allowed. If you win, the prize is $7000. What is the expected value of this lottery?

Accepted Answer

The total number of possible outcomes when picking five digits from 0 to 9 with duplicates allowed is $10^5 = 100,000$. The probability of winning is $1/100,000$. The expected value (EV) of the lottery can be calculated as follows: EV = (probability of winning * amount won) - (probability of losing * cost to play) = $(1/100,000 * $7000) - ((100,000-1)/100,000 * $1)$ = $$0.07 - $0.99999$ ≈ $-$0.93$.

Question 17

Obtain the population standard deviation,σ, for the given data. Assume that the data represent population data. Round
your final answer to one more decimal place than that used for the observations.
-The number of years of teaching experience is given below for 12 high-school teachers. 
4 16 10 6 12 19
17 8 5 13 22 31

Accepted Answer

The answer of Obtain the population standard deviation,σ, for the...

Question 18

Solve the problem.
-The table shows the total amount of precipitation (in inches) in a certain US city in 17 different years. Find the interquartile range.

Accepted Answer

The answer of Solve the problem.
-The table shows the total...

Question 19

Solve the problem.
-On a multiple choice test with 12 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Accepted Answer

The mean number of correct answers for guessing on a 12-question test, where each question has 4 options and only one correct answer, is calculated as 12 * (1/4) = 3. This is because the probability of guessing any single question correctly is 1/4, and over 12 questions, this averages to 3 correct answers.

Question 20

Solve the problem.
-On a multiple choice test with 20 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula: √(n * p * (1-p)), where n is the number of trials (20 questions), and p is the probability of success (1/4 for each question). Thus, the standard deviation is √(20 * 0.25 * 0.75) = √3.75 ≈ 1.9.

Quiz 10: Statistics and Probability

Find the normal probability using a grapher. -P(z < 1.5)

Obtain the population standard deviation,σ, for the given data. Assume that the data represent population data. Round your final answer to one more decimal place than that used for the observations. -The test scores of 9 students are listed below. 47 73 74 79 77 73 75 53 43

Solve the problem. -What is the probability that 12 rolls of a die will show exactly three sixes?

Solve the problem. -The total distances (in miles) cycled by sixteen athletes in the week prior to a cycling race are shown below. Find the interquartile range. 787 644 820 676 475 603 525 663 568 693 875 501 590 460 562 490

Solve the problem. -The test scores of 19 students are listed below. Find the interquartile range.

Solve the problem. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 18. Find the standard deviation for the number of seeds germinating in each batch.

Solve the problem. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 3. Find the mean for the number of seeds germinating in each batch.

Find the normal probability using a grapher. -P(z > -1.25)

Solve the problem. -What is the probability that 15 flips of a coin will show exactly 7 tails?

Solve the problem. -You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $42, otherwise you lose $30. What is your expected value for the game?

Find the normal probability using a grapher. -P(z < 1.25)

Solve the problem. -The star of the college basketball team has a 70% foul shooting average. If the player attempts 5 foul shots in a game, what is the probability that they will make at least 4 foul shots?

Solve the problem. -Suppose that there is a lottery that cost $1 to play. You must pick five digits in order from 0 to 9 and duplicates are allowed. If you win, the prize is $7000. What is the expected value of this lottery?

Solve the problem. -The table shows the total amount of precipitation (in inches) in a certain US city in 17 different years. Find the interquartile range.

Solve the problem. -On a multiple choice test with 12 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Solve the problem. -On a multiple choice test with 20 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.