3/2(4x – 1) – 3x = 5/4 – (x + 2)
1 answer:
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Answer:
0.64%.
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 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.
Mean of 75 grams and a standard deviation of 22 grams.
This means that
Sample of 144:
This means that
More than 80 or less than 70:
Both are the same distance from the mean, so we find one probability and multiply by 2.
The probability that it is less than 70 is the pvalue of Z when X = 70. So
By the Central Limit Theorem
has a pvalue of 0.0032
2*0.0032 = 0.0064.
0.0064*100% = 0.64%
The probability is 0.64%.
<u>Given</u>:
The given ratio is
We need to determine three ratios that are equivalent to the given ratio.
<u>Option A</u>:
The given ratio is
Let us divide the given ratio by 2.
Thus, we have;
Hence, the expression is equivalent to
Thus, Option A is the correct answer.
<u>Option B</u>:
The number 32 goes by 16 in 2 times and the number 24 goes by 12 in 2 times.
Thus, multiplying the ratio by 2, we get;
Thus, the expression is equivalent to
Hence, Option B is the correct answer.
<u>Option C</u>:
Let us divide the given ratio by 4.
Thus, we have;
Thus, the expression is equivalent to
Hence, Option C is the correct answer.
<u>Option D</u>:
The number 12 goes by 16 in times and the number 8 goes by 12 in
times.
The ratios are multiplied by different numbers.
Thus, the expression is not equivalent to
Hence, Option D is not the correct answer.
<u>Option E</u>:
The number 24 goes by 16 in 1.5 times and the number 16 goes by 12 in 0.75 times.
The ratios are multiplied by different numbers.
Thus, the expression is not equivalent to
Hence, Option E is not the correct answer.
Therefore, the equivalent ratios are Option A, B and C