3.
1 answer:
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Answer:
Step-by-step explanation:
4x -10y= 40
Let's rewrite this equation in the slope-intercept form (y= mx +c) so that we can obtain it's slope.
10y= 4x -40
Divide both side by 10:
The product of the gradients of perpendicular lines is -1.
⅖(gradient of line)= -1
Gradient of perpendicular line
Answer:
96.33% probability that everyone who appears for the flight will get a seat
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 everyone who appears for the flight will get a seat
100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So
has a pvalue of 0.9633
96.33% probability that everyone who appears for the flight will get a seat
By definition of the binomial coefficient,
so we have
as required.