Answer:
The Value of x is 10.
Step-by-step explanation:
Consider ABCD is a Parallelogram where
∠BCA = 43°
∠CBA = 98°
∠ACD = (2x+9)
To Find:
x = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
In ΔABC
Now CD || BA .......opposite sides of Parallelogram is parallel
.........Alternate Angles are equal
Substituting the values we get
The Value of x is 10.
Answer:
99.74% probability that the sample proportion will be less than 0.1
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that the sample proportion will be less than 0.1
This is the pvalue of Z when X = 0.1*276 = 27.6. So
has a pvalue of 0.9974
99.74% probability that the sample proportion will be less than 0.1