Answer:
a) probability that the sample will have between 50% and 60% of the identification correct = 0.498
b) The probability is 90% that the sample percentage is contained 45.5% and 54.5% of the population percentage
c) Probability that the sample percentage of correct identifications is greater than 65% = 0.01
Step-by-step explanation:
Sample size, n = 200
Since the brands are equally likely, p = 0.5, q = 0.5
The Standard deviation, ![\sigma_p = \sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=%5Csigma_p%20%3D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
![\sigma_p = \sqrt{\frac{0.5 * 0.5}{200} } \\\sigma_p = 0.0353](https://tex.z-dn.net/?f=%5Csigma_p%20%3D%20%5Csqrt%7B%5Cfrac%7B0.5%20%2A%200.5%7D%7B200%7D%20%7D%20%5C%5C%5Csigma_p%20%3D%200.0353)
a) probability that the sample will have between 50% and 60% of the identification correct.
![P(0.5 < X < 0.6) = P(\frac{0.5 - 0.5}{0.0353} < Z < \frac{0.6 - 0.5}{0.0353} )\\P(0.5 < X < 0.6) = P( 0 < Z < 2.832)\\P(0.5 < X < 0.6) = P(Z < 2.832) - P(Z < 0)\\P(0.5 < X < 0.6) = 0.998 - 0.5\\P(0.5 < X < 0.6) = 0.498](https://tex.z-dn.net/?f=P%280.5%20%3C%20X%20%3C%200.6%29%20%3D%20%20P%28%5Cfrac%7B0.5%20-%200.5%7D%7B0.0353%7D%20%3C%20Z%20%3C%20%5Cfrac%7B0.6%20-%200.5%7D%7B0.0353%7D%20%29%5C%5CP%280.5%20%3C%20X%20%3C%200.6%29%20%3D%20P%28%200%20%3C%20Z%20%3C%202.832%29%5C%5CP%280.5%20%3C%20X%20%3C%200.6%29%20%3D%20P%28Z%20%3C%202.832%29%20-%20P%28Z%20%3C%200%29%5C%5CP%280.5%20%3C%20X%20%3C%200.6%29%20%3D%200.998%20-%200.5%5C%5CP%280.5%20%3C%20X%20%3C%200.6%29%20%3D%200.498)
Probability that the sample will have between 50% and 60% of the identification correct is 0.498
b) p = 90% = 0.9
Getting the z value using excel:
z = (=NORMSINV(0.9) )
z = 1.281552 = 1.28 ( 2 dp)
Then we can calculate the symmetric limits of the population percentage as follows:
![z = \frac{X - \mu}{\sigma_p}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma_p%7D)
![-1.28 = \frac{X_1 - 0.5}{0.0353} \\-1.28 * 0.0353 = X_1 - 0.5\\-0.045+ 0.5 = X_1\\X_1 = 0.455](https://tex.z-dn.net/?f=-1.28%20%3D%20%5Cfrac%7BX_1%20-%200.5%7D%7B0.0353%7D%20%5C%5C-1.28%20%2A%200.0353%20%3D%20X_1%20-%200.5%5C%5C-0.045%2B%200.5%20%3D%20X_1%5C%5CX_1%20%3D%200.455)
![1.28 = \frac{X_2 - 0.5}{0.0353} \\1.28 * 0.0353 = X_2 - 0.5\\0.045+ 0.5 = X_2\\X_2 = 0.545](https://tex.z-dn.net/?f=1.28%20%3D%20%5Cfrac%7BX_2%20-%200.5%7D%7B0.0353%7D%20%5C%5C1.28%20%2A%200.0353%20%3D%20X_2%20-%200.5%5C%5C0.045%2B%200.5%20%3D%20X_2%5C%5CX_2%20%3D%200.545)
The probability is 90% that the sample percentage is contained 45.5% and 54.5% of the population percentage
c) Probability that the sample percentage of correct identifications is greater than 65%
P(X>0.65) = 1 - P(X<0.65)
![P(X](https://tex.z-dn.net/?f=P%28X%3C0.65%29%20%3D%20P%28Z%3C%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D%20%29%5C%5CP%28X%3C0.65%29%20%3D%20P%28Z%3C%20%5Cfrac%7B0.65%20-%200.5%7D%7B0.0353%7D%20%29%5C%5CP%28X%3C0.65%29%20%3D%20P%28Z%20%3C%204.2372%29%20%3D%200.99%5C%5CP%28X%3E0.65%29%20%3D%201%20-%20P%28X%3C0.65%29%5C%5CP%28X%3E0.65%29%20%3D%201%20-%200.99%5C%5CP%28X%3E0.65%29%20%3D%200.01)
Patty because she has the lowest time out of them all. From least to greatest Patty would be the least with her time being shorter than the rest
If you jumped from 20 feet up you would drop 30 feet.
Step-by-step explanation:
When we compare 2 system of equations (of the form y = mx + c), we take note of the following things:
- If the values of m and c in both equations are the same, they have infinitely many solutions
- If only the value of m is the same, they have no solutions
- If neither is the same, they have 1 solution
Bearing this in mind, we have the following answers:
y = -6x - 2 and y = -6x - 2
=> Infinitely many solutions
y = 0.5x + 5 and y = 0.5x + 1
=> No solutions
y = 0.25x + 2 and y = 5x - 4
=> 1 solution
y = 2x + 3 and y = 4x - 1
=> 1 solution
y = 2x + 5 and y = 2x + 5
=> Infinitely many solutions
y = -x - 3 and y = -x + 3
=> No solutions
Step-by-step explanation:
22/40 = 11/20 = (11 * 5)/(20 * 5) = 55/100.