Number 3 and how you got the answer
1 answer:
You might be interested in
Answer:
The probability is 0.789
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 normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, 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.
In this problem, we have that:
Find the probability that the mean age of the individuals sampled is within one year of the mean age for all individuals in the city.
Using , this is the pvalue of Z when X = 31 subtracted by the pvalue of Z when X = 29. So
X = 31
By the Central Limit Theorem
has a pvalue of 0.8944
X = 29
has a pvalue of 0.1056
0.8944 - 0.1056 = 0.7888
Rounded to three decimal places, 0.789
The probability is 0.789
Option D: 21 in is the base length of the triangular base.
Explanation:
Given that a triangular pyramid with a height of 9 inches has a volume of 63 cubic inches.
The height of the triangular base is 6 inches.
We need to determine the base length of the triangular pyramid.
The base length of the triangular pyramid can be determined using the formula,
Substituting and
in the above formula, we get,
Simplifying the terms, we get,
Dividing both sides by 3, we have,
Thus, the base length of the triangular pyramid is 21 in
Hence, Option D is the correct answer.