A cliff forms an angle of x∘ with a lake. If you stand on the edge of the cliff and throw a rock at a distance of 48 ft to the w
ater, the rock will strike the water about 5 ft from the base of the cliff. What is measure of the angle that the cliff forms with the lake? Round your answer to the nearest whole degree.
1 answer:
Answer:
∅=6°
Step-by-step explanation:
we have that the distance from the edge of the cliff to the lake is 48 feet, and when the stone is thrown into the lake it collides with the water 5 feet from the base of the cliff so you must find the distance that the stone travels from the edge of the sewer up to 5 feet beyond its base (hypotenuse) and then the angle that forms it (slope)
Hypotenuse (c)
:
Slope ∅
Sin∅ = 5ft/48.25ft = 0.1036
∅=arcsin(0.1036) ≅ 5.9°, but how should we round to the nearest integer
, then:
∅=6°
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Answer:
P(939.6 < X < 972.5) = 0.6469
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.
This means that
Sample of 57:
This means that
Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.
This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So
X = 972.5
By the Central Limit Theorem
has a pvalue of 0.6915
X = 939.6
has a pvalue of 0.0446
0.6915 - 0.0446 = 0.6469
So
P(939.6 < X < 972.5) = 0.6469