A new car is purchased for 24900 dollars. The value of the car depreciates at 6.75% per year. To the nearest tenth of a year, ho
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Answer:
97.74% probability that the sample mean would differ from the true mean by less than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
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 random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the sample mean would differ from the true mean by less than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected?
This is the pvalue of Z when X = 29 + 1.9 = 30.9 subtracted by the pvalue of Z when X = 29 - 1.9 = 27.1. So
X = 30.9
By the Central Limit Theorem
has a pvalue of 0.9887
X = 27.1
has a pvalue of 0.0113
0.9887 - 0.0113 = 0.9774
97.74% probability that the sample mean would differ from the true mean by less than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
Answer:
Step-by-step explanation:
step 1
Find the area of complete circle
The area of the circle is given by the formula
we have
substitute
step 2
Find the area of the shaded region
we know that
The area of complete circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of the shaded region if the central angle is equal to 80 degrees