Probability and Statistics
2 answers:
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Answer:
34°
Step-by-step explanation:
The law of cosines is good for finding angles when only sides are known. We'll use the conventional sides a, b, c, and angles A, B, C. Yes, we know the problem statement calls the smallest angle "J". We trust you can make the translation.
a² = b² +c² -2bc·cos(A) . . . . . for sides a, b, c and angle A
Solving for the angle, we get ...
A = arccos((b² +c² -a²)/(2bc))
Filling in the numbers with "a" being the shortest side, we have ...
A = arccos((13² +19² -11²)/(2·13·19)) = arccos(409/494)
A ≈ 34.113°
The smallest angle, ∠J, is about 34°.
Answer:
Step-by-step explanation:
Hello!
To evaluate the market for a new car charger, a market researcher surveyed 600 customers and found out that 73% of them own a car.
The parameter of interest is the population proportion and the study variable is "the number of customers that own a car out of 600".
Using the Central Limit Theorem you can approximate the distribution of the sampling proportion to normal:
p'≈N(p;)
Where p' is the sample proportion
p is the population proportion and the mean of the distribution
is the variance of the distribution
Then de standard deviation of the samplig proportion distribution is
You can estimate it using the sample proportion:
Using the same sample proportion but a sample size of n=150, the estimated standard deviation is:
I hope it helps!