Using the Empirical Rule and the Central Limit Theorem, we have that:
- About 68% of the sample mean fall with in the intervals $1.64 and $1.82.
- About 99.7% of the sample mean fall with in the intervals $1.46 and $2.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
<h3>What does the Central Limit Theorem state?</h3>
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem, the standard deviation of the distribution of sample means is:

68% of the means are within 1 standard deviation of the mean, hence the bounds are:
99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:
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The 4th one goes with the 1st box
The 2nd one goes with the 2nd box
The last one goes with the 3rd box
The two options that are the possible first step to begin to simplify the equation are (c) Multiply both sides of the equation by –2. and (d). Distribute Negative one-half over (x + 4).
<h3>How to determine which two options are the possible first step to begin to simplify the equation?</h3>
The equation is given as:
Negative one-half (x + 4) = 6
Rewrite the above equation properly
So, we have
-1/2(x + 4) = 6
A possible first step is to multiply both sides of the equation -1/2(x + 4) = 6 by -2
So, we have
x + 4 = -12
Another possible first step is to distribute the expression -1/2(x + 4) in the equation
So, we have
-1/2x - 1/2 * 4 = 6
Hence, the two options that are the possible first step to begin to simplify the equation are (c) Multiply both sides of the equation by –2. and (d). Distribute Negative one-half over (x + 4).
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four and negative four :)