1) We have that there are (52,3) ways to pick 3 cards out of 52 cards. Also, there are (4,3) ways to pick 3 kings out of the 4 total available kings in the deck. In essence, we need to have one of those ways to be the selected 3 cards. Hence, the probability is the ration (4,3)/(52,3). Computing this:
P=

The probability is very low but not negligible.
2) The Pascal triangle defines a recursive relationship. Hence, we would need to calculate all the binomial coefficients up to 51. Thus, it is not at all practical to use the Pascal Triangle to calculate the ways. It is easier to do the direct computation.
Let x = price of shoes
Then price of jacket would be x - 5.81
Combining the two would give you
x + x - 5.81 = 99.15
combining like terms simplifies to 2x - 5.81 = 99.15;
now adding 5.81 to both sides of the equal sign leaves
2x = 104.96
and finally, dividing both sides by 2, gives x = $52.48; which is the cost of the shoes. Recall, the cost of the jacket is 5.81 less than the cost of the shoes.
so, COST OF THE JACKET is 52.48 - 5.81 = $46.67
Answer:
The 95% confidence interval for the population variance is ![\left[0.219, \hspace{0.1cm} 0.807\right]\\\\](https://tex.z-dn.net/?f=%5Cleft%5B0.219%2C%20%5Chspace%7B0.1cm%7D%200.807%5Cright%5D%5C%5C%5C%5C)
The 95% confidence interval for the population mean is ![\left [15.112, \hspace{0.3cm}15.688\right]](https://tex.z-dn.net/?f=%5Cleft%20%5B15.112%2C%20%5Chspace%7B0.3cm%7D15.688%5Cright%5D)
Step-by-step explanation:
To solve this problem, a confidence interval of
for the population variance will be calculated.

Then, the
confidence interval for the population variance is given by:
Thus, the 95% confidence interval for the population variance is:![\\\\\left [\frac{(19-1)(0.6152)^2}{32.852}, \hspace{0.1cm}\frac{(19-1)(0.6152)^2}{8.907} \right ]=\left[0.219, \hspace{0.1cm} 0.807\right]\\\\](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5Cleft%20%5B%5Cfrac%7B%2819-1%29%280.6152%29%5E2%7D%7B32.852%7D%2C%20%5Chspace%7B0.1cm%7D%5Cfrac%7B%2819-1%29%280.6152%29%5E2%7D%7B8.907%7D%20%5Cright%20%5D%3D%5Cleft%5B0.219%2C%20%5Chspace%7B0.1cm%7D%200.807%5Cright%5D%5C%5C%5C%5C)
On other hand,
A confidence interval of
for the population mean will be calculated

\
Thus, the 95\% confidence interval for the population mean is:![\\\\\left [15.40 - 2.093\sqrt{\frac{(0.6152)^2}{19}}, \hspace{0.3cm}15.40 + 2.093\sqrt{\frac{(0.6152)^2}{19}} \right ]=\left [15.112, \hspace{0.3cm}15.688\right] \\\\](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5Cleft%20%5B15.40%20-%202.093%5Csqrt%7B%5Cfrac%7B%280.6152%29%5E2%7D%7B19%7D%7D%2C%20%5Chspace%7B0.3cm%7D15.40%20%2B%202.093%5Csqrt%7B%5Cfrac%7B%280.6152%29%5E2%7D%7B19%7D%7D%20%5Cright%20%5D%3D%5Cleft%20%5B15.112%2C%20%5Chspace%7B0.3cm%7D15.688%5Cright%5D%20%5C%5C%5C%5C)