Find the value of a that makes the statement true. 3^-1 ÷ 3^4 = 3^a .A = ?
2 answers:
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Answer:
To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.
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 sums, we have that the mean is and the standard deviation is
In this problem, we have that:
This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.
X = 4000
By the Central Limit Theorem
has a pvalue of 0.9991
X = 3000
has a pvalue of 0.0009
0.9991 - 0.0009 = 0.9982
So the correct answer is:
To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.
The completed statement are:
- Angle UZT is congruent to angle TZY.
- Angle VZW is congruent to angle YZX.
Part A:
Angle UZT is congruent to angle TZY.
Using the image attached figure, we can see that:
∠UZT = 54°
∠TZY = 54°
Hence one can say that ∠TZY = ∠UZT are both congruent angles.
Part B:
Angle VZW is congruent to angle YZX.
Using the image attached attached, we can see that:
∠VZW = 71°
∠YZX = 71°
Hence, ∠YZX = ∠VZW are both regarded as congruent angles .
Therefore, The completed statement are:
- Angle UZT is congruent to angle TZY.
- Angle VZW is congruent to angle YZX.
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