Yolanda wanted to see if there was a connection between red hair and green eyes. She observed people walking past her on the str
eet and noted their hair and eye color.
Red Hair
Green eyes: 18
Eye color other than green: 29
Hair Color Other Than Red
Green eyes: 114
Eye color other than green: 650
Consider the relative frequency table.
To the nearest whole percent, what is the value of x in the table?
A) x = 14%
B) x = 15%
C) x = 16%
D) x = 18%
Red Hair
Green eyes: 18
Eye color other than green: 29
Hair Color Other Than Red
Green eyes: 114
Eye color other than green: 650
Consider the relative frequency table.
To the nearest whole percent, what is the value of x in the table?
A) x = 14%
B) x = 15%
C) x = 16%
D) x = 18%
2 answers:
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Answer:
There is a 99.24% probability that Claude's sample has a mean between 119.985 and 120.0125 inches.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
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.
In this problem, we have that:
The population of rods has a mean length of 120 inches and a standard deviation of 0.05 inch. This means that .
Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. This means that .
The probability that Claude's sample has a mean between 119.985 and 120.0125 inches is
We are working with the sample mean, so we use the standard deviation of the sample, that is, instead of
in the z score formula.
This probability is the pvalue of Z when subtracted by the pvalue of Z when
.
X = 120.0125
has a pvalue of 0.9938.
X = 119.985
has a pvalue of 0.0014.
So there is a 0.9938 - 0.0014 = 0.9924 = 99.24% probability that Claude's sample has a mean between 119.985 and 120.0125 inches.
Answer:
Step-by-step explanation:
we know that
The number of kWh of energy that the model house generate per year is given by the sum of kWh of energy generates by the windmills multiplied by the number of windmills, plus the kWh of energy generates by the solar panels multiplied by the number of solar panels.
so
For 10 year
Multiply the expression above by 10
Apply distributive property
Solution:
Consider the Given Isosceles Triangle
Considering the Possibilities
Case 1. When two equal angles are of 70°
Let the third angle be x.
Keeping in mind , that sum of Interior angles of Triangle is 180°.
70° + 70° + x= 180°
140° +x= 180°
x= 180°- 140°
x= 40°
Case 2:
When an angle measures 70°, and two equal angles measure x°.
Keeping the same property of triangle in mind, that is sum of interior angles of triangle is 180°.
70° + x° + x° = 180°
⇒ 70° + 2 x° = 180°
⇒ 2 x° = 180° - 70°
⇒ 2 x° = 110°
Dividing both sides by 2, we get
x= 55°
