Statistics Solutions

SAT scores are normally distributed with a mean of 1000 and a standard deviation of 150. Use this scenario to answer the following questions. What is the probability that a randomly selected student scored higher than 1020? Round to the nearest ten-thousandth (four decimal places). Question Blank 1 of 4 type your answer... What is the probability that a group of 25 randomly selected students have an average SAT score higher than 1020? Round to the nearest ten-thousandth (four decimal places). Question Blank 2 of 4 type your answer... What is the probability that a group of 25 randomly selected students have an average SAT score lower than 950? Round to the nearest ten-thousandth (four decimal places). Question Blank 3 of 4 type your answer... What is the probability that a group of 25 randomly selected students have an average SAT score between 950 and 1020? Round to the nearest ten-thousandth (four decimal places). Question Blank 4 of 4 type your answer... Question at position 3 3 Fill in the Blank 22 points Question at position 3 SAT scores are normally distributed with a mean of 1000 and a standard deviation of 150. Use this scenario to answer the following questions. Find the mean of the sampling distribution of sample means for a sample size of 200. Question Blank 1 of 2 type your answer... Find the standard deviation of the sampling distribution of sample means for a sample size of 200. Round your answer to three decimal places. Question Blank 2 of 2 type your answer...

Answer: Q1: P(X > 1020) = 0.4470 | Q2: P(x̄ > 1020, n=25) = 0.2525 |

Oct 13, 2026

A lifeguard counts the number of swimmers in the pool when she starts her shift and notes the temperature. The equation of the regression line for the data in the table is y^ = 1.62x - 105.5, where x represents the temperature and y^ is the number of swimmers. Day | Temperature (°F) | Number of swimmers Monday | 85 | 32 Tuesday | 90 | 40 Wednesday | 92 | 41 Thursday | 88 | 39 Friday | 95 | 50 What is the meaning of 1.62 in the equation?

Answer: The 1.62 is the slope. It means that for every 1°F increase

Oct 1, 2026

Which graph shows a strong positive correlation?

Answer: The correct graph shows a scatter plot where points are tigh

Oct 1, 2026

The residuals for data set A and data set B were calculated for a linear model and plotted on separate residual plots. The residuals for data set A form a pattern. The residuals for data set B do not form a pattern. A linear model would be a good fit for which data set(s)?

Answer: Data set B. Because its residuals show no pattern (random sc

Oct 1, 2026

Penny recorded the hours she worked as a waitress and how much money she earned in tips. This scatterplot shows her results. Based on the line of best fit, which statement is true? The line of best fit passes through points (2, 20) and (8, 80). Answer choices: - As the number of hours worked increases by 1 hour, the amount of tip money earned increases by $10. - As the number of hours worked increases by 1 hour, the amount of tip money earned increases by $20. - The initial amount of tip money is $2. - The initial amount of tip money is $10.

Answer: As the number of hours worked increases by 1 hour, the amoun

Oct 1, 2026

In an experiment, a ball is drawn from an urn containing 13 green balls and 7 red balls. If the ball is green, three coins are tossed. Otherwise two coins are tossed. How many elements of the sample space will have a green ball? How many elements of the sample space are there altogether?

Answer: Green-ball elements: $13 \times 8 = \mathbf{104}$. Total sam

Sep 30, 2026

A student chooses 4 books at random from a reading list of 11 books.

Answer: $C(11,4) = 330$ different combinations of books

Sep 1, 2026

11, 14, 22, 19, 23, 22, 22 Find the mean, median, mode, range, variance, and standard deviation.

Answer: Mean = 19 | Median = 22 | Mode = 22 | Range = 12 | Variance

Aug 18, 2026

You are a robotics engineer working for a large tech company. For one of your artificially intelligent robots, you are looking to see if the size of the data file used to train the robot is predictive of the time the robot takes to complete a maze. You are going to collect a random sample of 7 attempts at completing the maze. You will note for each attempt the size of the data file (denoted by x, in MB) and the time (denoted by y, in seconds) to complete the maze. You will also note the product x*y of the size of the data file and the completion time for each attempt. Data file size, x (in MB): 123.8, 99.6, 198.1, 42.5, 61.3, 164.2, 85.4 Completion time, y (in seconds): 134, 253, 85, 386, 423, 157, 226 xy: 16,589.2, 25,198.8, 16,838.5, 16,405, 25,929.9, 25,779.4, 19,300.4 Find: n, x_bar, y_bar, s_x, s_y, sum(xy) Then compute: - Sample correlation coefficient r - Slope b_1 - y-intercept b_0 - Regression equation: y_hat = b_0 + b_1*x

Answer: $n = 7$, $\bar{x} \approx 110.7$ MB, $\bar{y} \approx 237.7$

Jun 18, 2026