Norma Ann planned a rectangular courtyard, as shown in the scale drawing below. She decides to change the width, the shorter sid
1 answer:
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Answer:
0.13% probability that this selected sample has an average thickness greater than 53
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
.
In this problem, we have that:
What is the probability that this selected sample has an average thickness greater than 53?
This is 1 subtracted by the pvalue of Z when X = 53. So
By the Central Limit Theorem
has a pvalue of 0.9987
1 - 0.9987 = 0.0013
0.13% probability that this selected sample has an average thickness greater than 53
Answer:
the answer is hours
Step-by-step explanation:
so first we have to turn the fractions into mixed fractions, in order to do that we multiply the whole number by the denominator and add the numerator, our answer becomes the new numerator over the same denominator.
3 x 4 + 3
12 + 3
15
we do the same thing again.
1 x 3 + 1
3 + 1
4
then after we get our mixed fractions we subtract them from each other. Since the denominators are not the same we multiply to get the same denominators.
we subtract the numerators and keep the denominators.
then we simplify.