A footbridge is in the shape of an arc of a circle. The bridge is 7 ft tall and 29 ft wide. What is the radius of the circle tha
t contains the bridge? Round your answer to the nearest tenth.
1 answer:
Answer:
18.5 ft (to the nearest tenth)
Step-by-step explanation:
The diameter of the circle passes through the center of the circle and divides the width of the circle into two equal parts.
We complete the circle and apply the <u>Law of Intersecting Chords.</u>
In the diagram, by this law:
AB X BC =DB X BE
7*x=14.5X14.5
x=14.5X14.5÷7
x=30.04
Therefore:
Length of the Diameter= 7+30.04 ft=37.04 ft
Radius =37.04/2= 18.5 ft
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Answer:
0.64%.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, 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.
Mean of 75 grams and a standard deviation of 22 grams.
This means that
Sample of 144:
This means that
More than 80 or less than 70:
Both are the same distance from the mean, so we find one probability and multiply by 2.
The probability that it is less than 70 is the pvalue of Z when X = 70. So
By the Central Limit Theorem
has a pvalue of 0.0032
2*0.0032 = 0.0064.
0.0064*100% = 0.64%
The probability is 0.64%.