A mile is 5,280 feet between which two integers is the elevation of the trench in miles-21,844 feet is between and miles
2 answers:
Answer:
21,844 feet is between 4 and 5 miles.
Step-by-step explanation:
We are asked to find two integers between which the elevation of the 21,844 feet trench lies in miles.
Let us convert 21,844 feet into miles by dividing 21,844 by 5,280 as 1 mile equals 5,280 feet.
We can see that 21,844 feet is equal to 4.137 miles, which is greater than 4 miles and less than 5 miles, therefore, 21,844 feet is between 4 and 5 miles.
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Answer:
The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.
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 establishes 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.
A distribution of values is normal with a mean of 60 and a standard deviation of 16.
This means that
Samples of size 25:
This means that
Find the interval containing the middle-most 76% of sample means.
Between the 50 - (76/2) = 12th percentile and the 50 + (76/2) = 88th percentile.
12th percentile:
X when Z has a p-value of 0.12, so X when Z = -1.175.
By the Central Limit Theorem
88th percentile:
The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.