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:
More can be learned about the Empirical Rule at brainly.com/question/24537145
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He needs to run with approximately 6429 for a distance of 9 km
<h3>How to determine the number of strides?</h3>
The given parameters are:
Length of stride = 1.4 m
Distance for marathon = 9 km
The number of strides needed is then calculated as:
Number of stride = Distance for marathon/Length of stride
Substitute the known values in the above equation
Number of stride = 9km/1.4m
Convert km to m
Number of stride = 9000m/1.4m
Evaluate the quotient
Number of stride = 6428.57143
Approximate the estimate
Number of stride = 6429
Hence, he needs to run with approximately 6429 for a distance of 9 km
Read more about quotients at:
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Because then it would be easier to get an answer for a problem
Answer:
Length of the room is 180 ft
Step-by-step explanation:
We have a rectangular room with dimensions:
width = 70 ft and length "x" (unknown)
Perimeter of a rectangle is 2*w + 2*x and according to problem statement 500 ft of lights will fit exactly in room perimeter then:
2*70 + 2*x = 500
140 + 2*x = 500
2*x = 500 - 140
2*x = 360
x = 360/2
x = 180 ft
