The dot plots below show the scores for a group of students who took two rounds of a quiz: Two dot plots are shown one below the other. The title for the dot plot on the top is Round 1 and the title for the bottom plot is Round 2. Below the line for each dot plot is written Score. There are markings from 5 to 9 on the line at intervals of one. There are 2 dots above the mark 5, 3 dots above the mark 6, 4 dots above the mark 7, and 1 dot above the mark 8. For the bottom dot plot there are 6 dots above the mark 6, 2 dots above the mark 8, and 2 dots above the mark 9. Which of the following inferences can be made using the dot plot? The range of each round is the same. There is no overlap between the data. Round 1 scores were higher than round 2 scores. Round 2 scores were lower than round 1 scores.

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is:

you can not solvr this without numbers

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.