Question

1. Draw a histogram from all the data. Starting at the bottom row, for each set of 10 flips, place an “x” in the column corresponding to the number of heads that set produced. Your histogram should look similar to the example below: 2. Calculate the mean and standard deviation. mean = _____, standard deviation = _____ 3. Calculate the percent of the data that is within 1, 2, and 3 standard deviations of the mean. within 1 standard deviation = _____% within 2 standard deviations = _____% within 3 standard deviations = _____% 4. Compare your results to a normal distribution. Interpret any differences.

Answer 1

To draw the histogram, calculate the mean and standard deviation, and analyze the data's relationship to a normal distribution

Step-by-step explanation:

To draw a histogram, you need to count the number of heads for each set of 10 flips and place an "x" in the corresponding column. Then, calculate the mean by adding up all the sums and dividing by the total number of sums. The standard deviation can be calculated using the formula. To calculate the percent of data within a certain number of standard deviations, you can use the empirical rule which states that approximately 68% of the data is within one standard deviation of the mean, 95% within two standard deviations, and more than 99% within three standard deviations. To compare your results to a normal distribution, you can check if the data follows the bell-shaped curve as expected or if there are significant differences.

Answer 2

Here is the histogram of the data:

[Image of a histogram with 10 bins, each representing the number of heads in a set of 10 flips. The most common number of heads is 5, and there are fewer heads and tails as the number of heads increases or decreases.]

The mean is 5 heads, and the standard deviation is 2.28.

Within 1 standard deviation of the mean are the values from 2.72 to 7.28. This includes 68.27% of the data.

Within 2 standard deviations of the mean are the values from 0.44 to 8.56. This includes 95.45% of the data.

Within 3 standard deviations of the mean are the values from -1.84 to 10.16. This includes 99.73% of the data.

The distribution of the data is close to normal, but there is a slight skew towards the left. This is because there are more sets of 10 flips with 5 heads than there are sets with 6 heads or 4 heads.

The normal distribution is a symmetrical distribution, which means that there is an equal amount of data above and below the mean. The distribution of the data in this case is slightly skewed, which means that there is more data below the mean than above the mean. This is because there are more sets of 10 flips with 5 heads than there are sets with 6 heads or 4 heads.

Step-by-step explanation: