Drew drives his car and Rachel drives her truck in the same direction on the highway at constant speeds for 3.25 hours. During t
1 answer:
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Answer:
0% probability that at least 1,500 will agree to respond
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 at least 1,500 will agree to respond
This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So
has a pvalue of 1.
1 - 1 = 0
0% probability that at least 1,500 will agree to respond
Answer:
a) 5.5
b) None
Step-by-step explanation:
The given data set is {96,89,79,85,87,94,96,98}
First we must find the mean.
We now find the absolute value of the distance of each value from the mean.
This is called the absolute deviation
{}
{}
We now find the mean of the absolute deviations
The least absolute deviation is 1.5. This is not within one absolute deviation.
Therefore none of the data set is closer than one mean absolute deviation away from the mean.