25 percent. in order to get only one face card you must get the ten and any other card. the probability of getting the 10 is 25 percent so that's the answe
Answer: 0.0016
Step-by-step explanation:
Given the following :
Population mean(m) = 196
Population Standard deviation (sd) = 32
Number of sample (n) = 18
Sample mean (x) = Total weight of sample / number of samples = 3928 / 18 = 218.2
Obtaining the test statistic (z) :
Z = [(x - m) / (sd/√n)]
Z = [(218.2 - 196) / (32/√18)]
Z = [(22.2 / 7.5424723)]
Z = 2.943
Hence,
P(Z > 2.94) = 1 - P(Z < 2.94)
= 1 - 0.9984
= 0.0016
let's firstly convert the mixed fractions to improper fractions.
![\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&\frac{7}{2}\\\\ x&\frac{7}{4} \end{array} \implies \cfrac{210}{x}=\cfrac{~~\frac{7}{2}~~}{\frac{7}{4}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bccll%7D%20%5Cstackrel%7Bsize%7D%7Bactual~miles%7D%26%5Cstackrel%7Bsize%7D%7Bmap~inches%7D%5C%5C%20%5Ccline%7B1-2%7D%20210%26%5Cfrac%7B7%7D%7B2%7D%5C%5C%5C%5C%20x%26%5Cfrac%7B7%7D%7B4%7D%20%5Cend%7Barray%7D%20%5Cimplies%20%5Ccfrac%7B210%7D%7Bx%7D%3D%5Ccfrac%7B~~%5Cfrac%7B7%7D%7B2%7D~~%7D%7B%5Cfrac%7B7%7D%7B4%7D%7D)
![\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B210%7D%7Bx%7D%3D%5Ccfrac%7B~~%5Cbegin%7Bmatrix%7D%207%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7B~~%5Cbegin%7Bmatrix%7D%202%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%5Ccdot%20%5Ccfrac%7B%5Cstackrel%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%204%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%7B~~%5Cbegin%7Bmatrix%7D%207%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%20%5Cimplies%20%5Ccfrac%7B210%7D%7Bx%7D%3D2%5Cimplies%20210%3D2x%5Cimplies%20%5Ccfrac%7B210%7D%7B2%7D%3Dx%5Cimplies%20105%3Dx)
