At a sale this week, a sofa is being sold for $272. This is a 36% discount from the original price. What is the original price?
1 answer:
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Answer:
0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.
Step-by-step explanation:
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
Probability that greater than 96 out of 153 DVDs will work correctly.
97 or more DVDs, which is 1 subtracted by the pvalue of Z when X = 97. So
has a pvalue of 0.6406
1 - 0.6406 = 0.3594
0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.
<u>Given</u>:
The quadratic equation is
We need to determine the solutions of the quadratic equation.
<u>Solution</u>:
Let us solve the equation to determine the value of x.
Adding both sides of the equation by 5x and 3, we get;
The solution of the equation can be determined using quadratic formula.
Thus, we get;
Thus, the two roots of the equation are and
Hence, the solutions of the equation are and