So we need to know the likelihood for each sum. the first sum is 2, and there is no way for one of the die to equal 6 if the sum is 2, therefore the probability is 0. The same applies when the sum is 3, 4, 5, and 6. Once the sum gets to 7, you must evaluate all possible options. For 7, your options are 1&6, 2&5, 3&4, 4&3, 5&2, 6&1, where the number before the ampersand is the first die, and the number after is the second. there is only one option of the 6 choices where the first die is 6, therefore the probability is 1/6. For 8, the options are 2&6, 3&5, 4&4, 5&3, 6&2. so of the 5 choices, there is only one option, therefore the probability is 1/5. For 9, the choices are 3&6, 4&5, 5&4, 6&3. So of the 4 choices, there is 1 option, therefore the probability is 1/4. For 10, the options are 4&6, 5&5, 6&4. Of the 3 choices, there is 1 option, therefore the probability is 1/3. For 11, the options are 5&6, 6&5. Of the 2 choices, there is 1 option, therefore the probability is 1/2. Finally, for 12, the only option is 6&6. There is only one choice, so the probability is 1.
I assume the solid is a "regular hexagonal prism", by which it means that the cross section is a regular hexagon with all sides and angles equal. Also, the exact apothem is 9.5262... but we will adopt the given value of 9.5.
First lateral surface area A1=6*side length*height=6*11*20=1320 units Then the end areas A2=2 faces * 6 triangles/face * [base * height (apothem) /2] =2*6*11*9.5/2 =627 units
The 90% confidence interval estimate of the mean of the population is between 6627 and 6941.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.761
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 6784 - 157 = 6627
The upper end of the interval is the sample mean added to M. So it is 6784 + 157 = 6941
The 90% confidence interval estimate of the mean of the population is between 6627 and 6941.