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Sylvia is twice as old as her brother. Find their ages now if in seven years her brother will be what her age was last year.
1 answer:
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Answer:
0.9452 = 94.52% probability that their mean length is less than 16.8 inches.
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 establishes 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 15.4 inches, and standard deviation of 3.5 inches.
This means that
16 items are chosen at random
This means that
What is the probability that their mean length is less than 16.8 inches?
This is the p-value of Z when X = 16.8. So
By the Central Limit Theorem
has a p-value of 0.9452.
0.9452 = 94.52% probability that their mean length is less than 16.8 inches.
Answer:
Step-by-step explanation:
Coordinates of Point b
b lies on the circle whose equation is
Comparing with the general form a circle with center at the origin:
The radius of the circle =17 which is the length of the hypotenuse of the terminal ray through point b.
For an angle drawn in standard position through point b,
x=-8 which is negative
y=15 which is positive
Therefore, the angle is in Quadrant II.