The park behind James's house used to have a bike trail that was 12.347 kilometers long. Last year, the trail was reduced to 9.4
2 answers:
Answer:
The difference in the lengths of the old and the new bike trails is 2.915 kilometers.
Step-by-step explanation:
The park behind James's house used to have a bike trail that was 12.347 kilometers long.
Last year, the trail was reduced to 9.432 kilometers to make space for a meditation garden.
So, the difference in lengths is = kilometers
Therefore, the difference in the lengths of the old and the new bike trails is 2.915 kilometers.
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Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).
In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It 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, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of
.
- The standard deviation is of
.
- Sample of 100, hence
The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:
Z = -2:
By the Central Limit Theorem
Z = 2:
The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).
You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213