Turner mesuares 3/4 foot of a ribbon for a coustume. He needs 9 pieces of ribbon with the same length
2 answers:
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Answer:
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Proportion of 0.6
This means that
Sample of 46
This means that
Mean and standard deviation:
Probability of obtaining a sample proportion less than 0.5.
p-value of Z when X = 0.5. So
By the Central Limit Theorem
has a p-value of 0.0838
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
If
then the derivative is
Critical points occur where . This happens for
In the first case, we find
In the second,
So all the critical points occur at multiples of , or
. (This includes all the even multiples of
.)
The values of a and b are 1/4 and 1/5 respectively
<h3>How to determine the true statement?</h3>The function is given as:
16x^2 - 25y^2 = 1
The above function is a horizontal hyperbola.
A horizontal hyperbola that passes through the origin is represented as:
Rewrite 16x^2 - 25y^2 = 1 as
By comparison, we have:
Solve for a and b
Hence, the values of a and b are 1/4 and 1/5 respectively
Read more about hyperbola at:
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