The Snow Sports Club from Sierra High School is boarding the tram at Heavenly Valley to ride up to the top of the mountain. The
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Answer:
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
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
A statistician calculates that 8% of Americans own a Rolls Royce.
This means that
Sample of 595:
This means that
Mean and standard deviation:
What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05. So
By the Central Limit Theorem
has a p-value of 0.0035
2*0.0035 = 0.0070
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
So.. if you notice the picture below
is really just 3/4 of a cylinder, or, a full cylinder, and then you slice 1/4 off of it
notice the right-angle in your picture at the bottom, is cut at a right-angle, meaning, the cutout is 1/4 of the volume
so
is really just 3/4 of a cylinder, or, a full cylinder, and then you slice 1/4 off of it
notice the right-angle in your picture at the bottom, is cut at a right-angle, meaning, the cutout is 1/4 of the volume
so
<u>Given</u>:
The measure of ∠ABD is (4x + 15)°
The measure of ∠DBC is (13x + 7)°
We need to determine the value of x.
<u>Value of x:</u>
Since, we know the property that every angle in a rectangle is 90°
Hence, the value of x can be determined by adding the two angles and equating to 90°
Thus, we have;
Substituting the values, we have;
Thus, the value of x is 4.