Answer:
a) P(x=5) = 0.2456
b) P(x≥6) = 0.3526
c) P(x<4) = 0.1887
Step-by-step explanation:
We can model this as a binomial experiment, with sample size n=10 and p=0.49.
To calculate the probability of having k subjects with very little confidence in the sample of 10, we solve:
![P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}](https://tex.z-dn.net/?f=P%28x%3Dk%29%20%3D%20%5Cdbinom%7Bn%7D%7Bk%7D%20p%5E%7Bk%7Dq%5E%7Bn-k%7D)
a) We have to calculate P(x=5).
For a binomial variable with n=10 and p=0.49, this can be calculated as:
![P(x=5) = \dbinom{10}{5} p^{5}q^{5}=252*0.0282*0.0345=0.2456\\\\](https://tex.z-dn.net/?f=P%28x%3D5%29%20%3D%20%5Cdbinom%7B10%7D%7B5%7D%20p%5E%7B5%7Dq%5E%7B5%7D%3D252%2A0.0282%2A0.0345%3D0.2456%5C%5C%5C%5C)
b) We have to calculate P(x≥6). This can be calculated as:
![P(x\geq6)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0138*0.0677=0.1966\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.0068*0.1327=0.1080\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0033*0.2601=0.0389\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0016*0.51=0.0083\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.0008*1=0.0008\\\\\\P(x\geq6)=0.1966+0.1080+0.0389+0.0083+0.0008\\\\P(x\geq6)=0.3526](https://tex.z-dn.net/?f=P%28x%5Cgeq6%29%3DP%28x%3D6%29%2BP%28x%3D7%29%2BP%28x%3D8%29%2BP%28x%3D9%29%2BP%28x%3D10%29%5C%5C%5C%5C%5C%5CP%28x%3D6%29%20%3D%20%5Cbinom%7B10%7D%7B6%7D%20p%5E%7B6%7Dq%5E%7B4%7D%3D210%2A0.0138%2A0.0677%3D0.1966%5C%5C%5C%5CP%28x%3D7%29%20%3D%20%5Cbinom%7B10%7D%7B7%7D%20p%5E%7B7%7Dq%5E%7B3%7D%3D120%2A0.0068%2A0.1327%3D0.1080%5C%5C%5C%5CP%28x%3D8%29%20%3D%20%5Cbinom%7B10%7D%7B8%7D%20p%5E%7B8%7Dq%5E%7B2%7D%3D45%2A0.0033%2A0.2601%3D0.0389%5C%5C%5C%5CP%28x%3D9%29%20%3D%20%5Cbinom%7B10%7D%7B9%7D%20p%5E%7B9%7Dq%5E%7B1%7D%3D10%2A0.0016%2A0.51%3D0.0083%5C%5C%5C%5CP%28x%3D10%29%20%3D%20%5Cbinom%7B10%7D%7B10%7D%20p%5E%7B10%7Dq%5E%7B0%7D%3D1%2A0.0008%2A1%3D0.0008%5C%5C%5C%5C%5C%5CP%28x%5Cgeq6%29%3D0.1966%2B0.1080%2B0.0389%2B0.0083%2B0.0008%5C%5C%5C%5CP%28x%5Cgeq6%29%3D0.3526)
c) We have to calculate P(x<4). That is:
![P(x](https://tex.z-dn.net/?f=P%28x%3C4%29%3DP%28x%3D0%29%2BP%28x%3D1%29%2BP%28x%3D2%29%2BP%28x%3D3%29%5C%5C%5C%5C%5C%5CP%28x%3D0%29%20%3D%20%5Cbinom%7B10%7D%7B0%7D%20p%5E%7B0%7Dq%5E%7B10%7D%3D1%2A1%2A0.0012%3D0.0012%5C%5C%5C%5CP%28x%3D1%29%20%3D%20%5Cbinom%7B10%7D%7B1%7D%20p%5E%7B1%7Dq%5E%7B9%7D%3D10%2A0.49%2A0.0023%3D0.0114%5C%5C%5C%5CP%28x%3D2%29%20%3D%20%5Cbinom%7B10%7D%7B2%7D%20p%5E%7B2%7Dq%5E%7B8%7D%3D45%2A0.2401%2A0.0046%3D0.0494%5C%5C%5C%5CP%28x%3D3%29%20%3D%20%5Cbinom%7B10%7D%7B3%7D%20p%5E%7B3%7Dq%5E%7B7%7D%3D120%2A0.1176%2A0.009%3D0.1267%5C%5C%5C%5C%5C%5CP%28x%3C4%29%3D0.0012%2B0.0114%2B0.0494%2B0.1267%5C%5C%5C%5CP%28x%3C4%29%3D0.1887)
Answer: The book costs $10 and the pen costs $4✔️
Step-by-step explanation:
Let B the cost of the book and let P the cost of the pen.
Then we know:
The book and the pen cost $14:
B + P = $14 } Equation 1
We also know:
The cost of the book is two dollars more than twice the cost of the pen.
B = 2P + $2 } Equation 2
Now we can substitute the value of B from the equation 2 in the equation 1:
2P + $2 + P = $14
3P = $14 - $2 = $12
P = $12/3 = $4 , cost of the pen
Since we know the value of B from the equation 2, we can calculate B:
B = 2P + $2 = 2x$4 + $2 = $8 + $2 = $10 , cost of the book
Answer: The book costs $10 and the pen costs $4✔️
<h3>Verify </h3>
We can substitute these values in equations 1 and 2 and check the results:
B + P = $14 } Equation 1
$10 + $4 = $14 ✔️check!
B = 2P + $2 } Equation 2
$10 = 2x$4 + $2 = $8 + $2 = $10 ✔️check!
<h2><em>Spymore</em></h2>
To find the tax = $3129 × 4% = $125.16.
The final price = $3129 + $125.16 = $3254.16.
Hope this helps
Answer:
thnks
Step-by-step explanation: