Given that x = 5.4 m and 0 = 26°, work out BC rounded to 3 SF.
1 answer:
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Answer:
-4.41
Step-by-step explanation:
208° is a 3rd-quadrant angle, so its x-coordinate will be negative. Your calculator can tell you that 5 times the cosine of this angle is -4.41, or you can refer to a diagram.
Answer:
a. X is the time, in seconds, of a randomly selected lap of Vogel.
b. X~N(129.01,2.26)
c. 67% of her laps that are completed in less than 130 seconds.
d. So the answer is 124.8 seconds.
e. The middle 80% of her laps are from 126.1 seconds to 131.9 seconds.
Step-by-step explanation:
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.
Terri Vogel, an amateur motorcycle racer, averages 129.01 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.26 seconds
This means that
a. In words, define the random variable X.
The problem states that X is the time, in seconds, of a randomly selected lap of Vogel.
b. X ~ ________(_____ , _____)
Normal with mean and standard deviation. So
X~N(129.01,2.26)
c. Find the percent of her laps that are completed in less than 130 seconds.
The proportion is the pvalue of Z when X = 130. So
has a pvalue of 0.67.
0.67*100% = 67%
67% of her laps that are completed in less than 130 seconds.
d. The fastest 3% of her laps are under
Under the 3rd percentile, which is X when Z has a pvalue of 0.03. So X when Z = -1.88.
So the answer is 124.8 seconds.
e. The middle 80% of her laps are from ___________seconds to ________seconds.
The 50 - (80/2) = 10th percentile to the 50 + (80/2) = 90th percentile.
10th percentile:
X when Z has a pvalue of 0.1, so X when Z = -1.28.
90th percentile:
X when Z has a pvalue of 0.9, so X when Z = 1.28.
The middle 80% of her laps are from 126.1 seconds to 131.9 seconds.