You are sitting on the ground flying a kite.
1 answer:
Answer:
Height of the kite = 36 feet
Step-by-step explanation:
Triangle attached in the figure shows the complete picture,
I am sitting at point A, string connecting the kite and me is side AC, height of the kite from the ground is side BC and side AB representing the distance between me and the kite.
Length of side BC = h
Length of side AC = 39 feet
Length of side AB = 15 feet
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
(39)² = (15)² + h²
h² = 1521 - 225
h² = 1296
h = √1296
h = 36 feet
Therefore, kite is at 36 feet height.
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Answer:
95.44% probability the resulting sample proportion is within .04 of the true proportion.
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 normally distributed samples are 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.
For the sampling distribution of the sample proportion in sample of size n, the mean is and the standard deviation is
In this question:
So
How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?
This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.
X = 0.24
By the Central Limit Theorem
has a pvalue of 0.9772.
X = 0.16
has a pvalue of 0.0228.
0.9772 - 0.0228 = 0.9544
95.44% probability the resulting sample proportion is within .04 of the true proportion.