Answer:
c. (12.12, 18.48)
Step-by-step explanation:
Hello!
The study variable is X: number of times a racehorse is raced during its career.
The average number is X[bar]= 15.3 and the standard deviation is S= 6.8 obtained from a sample of n=20 horses.
To estimate the population mean you need that the variable has a normal distribution, in this case, we have no information about its distribution so I'll assume that it has a normal distribution. With n=20 the most accurate statistic to use for the estimation is a Students-t for one sample, the formula for the interval is:
X[bar] ± 

[15.3 ± 2.093 *
]
[12.12; 18.48]
Using a significance level of 95% you'd expect that the true average of times racehorses are raced during their career is included in the interval [12.12; 18.48].
I hope it helps!
Answer:
[34,54]
Step-by-step explanation:
-The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.
Where:
- 68% is the first standard deviation
- 95% is the second standard deviation about the mean
- 99.7% is the 3rd standard deviation about the mean.
-Therefore. the middle 95% interval is calculated as:
![CI=\mu+2\sigma\\\\=44\pm 2(5)\\\\=44\pm 10\\\\=[34,54]](https://tex.z-dn.net/?f=CI%3D%5Cmu%2B2%5Csigma%5C%5C%5C%5C%3D44%5Cpm%202%285%29%5C%5C%5C%5C%3D44%5Cpm%2010%5C%5C%5C%5C%3D%5B34%2C54%5D)
Hence, the interval is [34,54]
Answer:
a = 39.2650873379cm
b = 11.5529459767cm
Step-by-step explanation:
a - Use the area of a triangle equation - 1/2 * a * b * Sin(C)
1/2 * 8 * 10 * Sin(79) = 39.2650873379cm
b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)
64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398
c = square root of 6.9396506484 = 11.5529459767cm
Put to however many significant figures / decimal places required.
:)
Eighty seven written in standard form would be...
80 + 7 = 87
Good Luck! :)
Answer:
Step-by-step explanation:
tan x° =
⇒<em> x°</em> ≈ 36.87° ≈ <em>36.9° </em>