2) If Michael invests $2000 in the bank at a rate of 5.5% for 6 years how much
1 answer:
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Answer:
0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
Step-by-step explanation:
To solve this question, we have 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
, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error
In this problem, we have that:
The standard deviation is the square root of the variance. So
What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
Either it differs by 104 or less dollars, or it differs by more than 104 dollars. The sum of the probabilities of these events is 100. I am going to find the probability that it differs by 104 or less dollars first.
Probability that it differs by 104 or less dollars first.
pvalue of Z when X = 16127 + 104 = 16231 subtracted by the pvalue of Z when X = 16127 - 104 = 16023. So
X = 16231
By the Central Limit Theorem
has a pvalue of 0.9970
X = 16023
has a pvalue of 0.0030
0.9970 - 0.0030 = 0.9940
99.40% probability that it differs by 104 or less.
What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
p + 99.40 = 100
p = 0.60
0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected
Answer:
2.2 metres squared
Step-by-step explanation:
We need to find the area of this trapezoid.
The area of a trapezoid is denoted by:
, where
and
are the parallel bases and h is the height
Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.
Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:
2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4
Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:
The answer is thus 2.2 metres squared.
<em>~ an aesthetics lover</em>