What is the value of n?
1 answer:
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Answer:
a) For this case we can use the fact that
And for this case since we ar einterested on and we know that the if we are below the y axis the sine would be negative then:
b) From definition we can use the fact that and we got this:
We can use the notabl angle and we know that :
Then we know that correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:
Step-by-step explanation:
For this case we can use the notable angls given on the picture attached.
Part a
For this case we can use the fact that
And for this case since we ar einterested on and we know that the if we are below the y axis the sine would be negative then:
Part b
From definition we can use the fact that and we got this:
We can use the notabl angle and we know that :
Then we know that correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:
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.