Mhanifa or Anyone answer this
2 answers:
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Answer:
a) P(7.99 ≤ X ≤ 8.01) = 0.8164
b) P(X ≥ 8.01) = 0.0475.
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 can be 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 can be approximated to a normal distribution with mean
In this problem, we have that:
(a) Calculate P(7.99 ≤ X ≤ 8.01) when n = 16.
n = 16, so
This probability is the pvalue of Z when X = 8.01 subtracted by the pvalue of Z when X = 7.99. So
X = 8.01
Applying the Central Limit Theorem
has a pvalue of 0.9082
X = 7.99
has a pvalue of 0.0918
0.9082 - 0.0918 = 0.8164
P(7.99 ≤ X ≤ 8.01) = 0.8164
(b) How likely is it that the sample mean diameter exceeds 8.01 when n = 25? P(X ≥ 8.01) =
n = 25, so
This is 1 subtracted by the pvalue of Z when X = 8.01. So
has a pvalue of 0.9525
1 - 0.9525 = 0.0475
P(X ≥ 8.01) = 0.0475.
Answer:
The height of the building is of 244.95 feet.
Step-by-step explanation:
We use the Pythagorean Theorem to solve this question.
We have that:
The shadow of 50 feet is one side of the right triangle, while the height h is other side.
The hypotenuse is the distance from the end of the shadow to the top of the building, which is 250 feet.
So
The height of the building is of 244.95 feet.